Scalinate di mattoni
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Re: Scalinate di mattoni
Se la base è di 6 mattoni per Min(m)=43 esiste la scalinata:
43
20…23
11…15…17
04…13…10…16
03…05…09…12…14
01…02…06…07…08…19
Dalle prove fatte sembrerebbe che il minimo sia questo.
(Oops... non ho messo i numeri in ordine decrescente...)
43
20…23
11…15…17
04…13…10…16
03…05…09…12…14
01…02…06…07…08…19
Dalle prove fatte sembrerebbe che il minimo sia questo.
(Oops... non ho messo i numeri in ordine decrescente...)
-
- Supervisore del sito
- Messaggi: 1747
- Iscritto il: ven mag 20, 2005 9:51 pm
- Località: Sestri Levante
- Contatta:
Re: Scalinate di mattoni
Giobimbo, ok, ci hai fatto uno scherzo, perché mi sembra che modificando leggermente la tua scalinata da 43 se ne possa ottenere un'altra da 42.
42
20-22
11-14-17
04-10-12-16
03-05-09-12-13
01-02-06-07-08-18
Anch'io ho lasciato i numeri in ordine crescente.
Salvo errori & omissioni.
Oops, c'è l'errore.
A questo punto mi piacerebbe dimostrare che con 42 è impossibile.
Pace e bene a tutti.
Gianfranco
Gianfranco
Re: Scalinate di mattoni
Mi dispiace deluderti ma faccio notare che hai messo due volte 12 .
Ecco la soluzione in ordine decrescente:
43
23…20
17…15…11
16…13…10…04
14…12…09…05…03
19…08…07…06…02…01
Le prime 4 file contengono 6+5+4+3=18 mattoni, i numeri vanno da 1 a 17 (manca solo il 18 sostituito dal 19), impossibile da migliorare, credo.
Ecco la soluzione in ordine decrescente:
43
23…20
17…15…11
16…13…10…04
14…12…09…05…03
19…08…07…06…02…01
Le prime 4 file contengono 6+5+4+3=18 mattoni, i numeri vanno da 1 a 17 (manca solo il 18 sostituito dal 19), impossibile da migliorare, credo.
-
- Supervisore del sito
- Messaggi: 1747
- Iscritto il: ven mag 20, 2005 9:51 pm
- Località: Sestri Levante
- Contatta:
Re: Scalinate di mattoni
Oops, ho visto e segnalato l'errore.
Grazie Giobimbo!
Grazie Giobimbo!
Pace e bene a tutti.
Gianfranco
Gianfranco
Re: Scalinate di mattoni
Pardon, solo adesso mi accorgo di quanto discusso sulla base da 6 e dell'errore di cui non mi ero accorto.
In effetti ero partito con il totale da 43, ma mi era sembrato che fosse possibile quello da 39, per cui ne avevo postato un unico esempio a titolo di curiosità, conscio del fatto che uno studio completo sarebbe stato troppo complicato con le centinaia di soluzioni possibili.
Ad ogni modo, a titolo di esempio, riprendendo la soluzione di Giobimbo, vediamo cosa ci si può ricare con qualche piccola modifica:
. .
.
APPARE EVIDENTE che se in cima sostituiamo 20 e 23 con 21 e 22, otteniamo altre 15 composizioni diverse
In effetti ero partito con il totale da 43, ma mi era sembrato che fosse possibile quello da 39, per cui ne avevo postato un unico esempio a titolo di curiosità, conscio del fatto che uno studio completo sarebbe stato troppo complicato con le centinaia di soluzioni possibili.
Ad ogni modo, a titolo di esempio, riprendendo la soluzione di Giobimbo, vediamo cosa ci si può ricare con qualche piccola modifica:
. .
.
APPARE EVIDENTE che se in cima sostituiamo 20 e 23 con 21 e 22, otteniamo altre 15 composizioni diverse
_________________
$\text { }$ciao ciao
E' la somma che fa il totale (Totò)
$\text { }$ciao ciao
E' la somma che fa il totale (Totò)
Re: Scalinate di mattoni
Pasquale, non so cosa sia successo nell'applicazione del tuo metodo, ma alcuni di questi schemi hanno righe che non fanno 43
(Bruno)
...........................
Invisibile un vento
l'ha apena sfioragia
sospension d'un momento;
e la bola iridessente gera 'ndagia.
{Biagio Marin}
................................................................
Meglio soluzioni sbagliate che risposte esatte.
{Rudi Mathematici}
...........................
Invisibile un vento
l'ha apena sfioragia
sospension d'un momento;
e la bola iridessente gera 'ndagia.
{Biagio Marin}
................................................................
Meglio soluzioni sbagliate che risposte esatte.
{Rudi Mathematici}
Re: Scalinate di mattoni
E' possibile che nel ricopiare dalla brutta abbia commesso qualche errore, o che abbia battuto un tasto per altro, o che l'ora tarda mi abbia obnubilato il cervello, ma spero che sia chiaro il procedimento. Grazie, vedo di fare un controllo.
_________________
$\text { }$ciao ciao
E' la somma che fa il totale (Totò)
$\text { }$ciao ciao
E' la somma che fa il totale (Totò)
Re: Scalinate di mattoni
Ho rifatto tutto ex novo per fare prima e spero di non aver commesso altri errori.
Se non vi sono errori, son venute fuori 2 soluzioni in più, per cui in totale , con l'alternativa del 22 e 21 in cima, abbiamo 34 soluzioni derivate tutte dalla prima.
Sono tutte soluzioni che si ottengono confrontando i numeri di ogni riga, presi due a due, con quelli delle altre righe, aventi la stessa somma.
Ci vuole tempo e attenzione, altrimenti possono venir fuori errori o doppioni.
Se non vi sono errori, son venute fuori 2 soluzioni in più, per cui in totale , con l'alternativa del 22 e 21 in cima, abbiamo 34 soluzioni derivate tutte dalla prima.
Sono tutte soluzioni che si ottengono confrontando i numeri di ogni riga, presi due a due, con quelli delle altre righe, aventi la stessa somma.
Ci vuole tempo e attenzione, altrimenti possono venir fuori errori o doppioni.
_________________
$\text { }$ciao ciao
E' la somma che fa il totale (Totò)
$\text { }$ciao ciao
E' la somma che fa il totale (Totò)
Re: Scalinate di mattoni
Cari ed ottimi, volevo solo dirvi
$\begin{array}{|c|c|c|c|c|c|c|C}
\hline
\mathtt{65} & & & & & & \\
\hline
\mathtt{39} & \mathtt{26} & & & & & \\
\hline
\mathtt{23} & \mathtt{22} & \mathtt{20} & & & & \\
\hline
\mathtt{18} & \mathtt{17} & \mathtt{16} & \mathtt{14} & & & \\
\hline
\mathtt{19} & \mathtt{13} & \mathtt{12} & \mathtt{11} & \mathtt{10} & & \\
\hline
\mathtt{21} & \mathtt{15} & \mathtt{09} & \mathtt{08} & \mathtt{07} & \mathtt{05} & \\
\hline
\mathtt{25} & \mathtt{24} & \mathtt{06} & \mathtt{04} & \mathtt{03} & \mathtt{02} & \mathtt{01} \\
\hline
\end{array}$
$\begin{array}{|c|c|c|c|c|c|c|C}
\hline
\mathtt{65} & & & & & & \\
\hline
\mathtt{39} & \mathtt{26} & & & & & \\
\hline
\mathtt{23} & \mathtt{22} & \mathtt{20} & & & & \\
\hline
\mathtt{18} & \mathtt{17} & \mathtt{16} & \mathtt{14} & & & \\
\hline
\mathtt{19} & \mathtt{13} & \mathtt{12} & \mathtt{11} & \mathtt{10} & & \\
\hline
\mathtt{21} & \mathtt{15} & \mathtt{09} & \mathtt{08} & \mathtt{07} & \mathtt{05} & \\
\hline
\mathtt{25} & \mathtt{24} & \mathtt{06} & \mathtt{04} & \mathtt{03} & \mathtt{02} & \mathtt{01} \\
\hline
\end{array}$
il panurgo
Principio di Relatività: $\mathbb{m} \not \to \mathbb{M} \, \Longleftrightarrow \, \mathbb{M} \not \to \mathbb{m}$
"Se la montagna non va a Maometto, Maometto NON va alla montagna"
Principio di Relatività: $\mathbb{m} \not \to \mathbb{M} \, \Longleftrightarrow \, \mathbb{M} \not \to \mathbb{m}$
"Se la montagna non va a Maometto, Maometto NON va alla montagna"
Re: Scalinate di mattoni
Bene, seguono alcune varianti derivate (a parte errori o ripetizoni) :
.
.
_________________
$\text { }$ciao ciao
E' la somma che fa il totale (Totò)
$\text { }$ciao ciao
E' la somma che fa il totale (Totò)
Re: Scalinate di mattoni
In realtà intendevopanurgo ha scritto: ↑lun apr 19, 2021 5:54 pmCari ed ottimi, volevo solo dirvi
$\begin{array}{|c|c|c|c|c|c|c|C}
\hline
\mathtt{65} & & & & & & \\
\hline
\mathtt{39} & \mathtt{26} & & & & & \\
\hline
\mathtt{23} & \mathtt{22} & \mathtt{20} & & & & \\
\hline
\mathtt{18} & \mathtt{17} & \mathtt{16} & \mathtt{14} & & & \\
\hline
\mathtt{19} & \mathtt{13} & \mathtt{12} & \mathtt{11} & \mathtt{10} & & \\
\hline
\mathtt{21} & \mathtt{15} & \mathtt{09} & \mathtt{08} & \mathtt{07} & \mathtt{05} & \\
\hline
\mathtt{25} & \mathtt{24} & \mathtt{06} & \mathtt{04} & \mathtt{03} & \mathtt{02} & \mathtt{01} \\
\hline
\end{array}$
$\vdots\\
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{18} & \mathtt{06} & & & \\
\hline \mathtt{16} & \mathtt{15} & \mathtt{14} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{17} & \mathtt{12} & \mathtt{07} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{18} & \mathtt{06} & & & \\
\hline \mathtt{16} & \mathtt{15} & \mathtt{14} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{17} & \mathtt{12} & \mathtt{07} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{18} & \mathtt{06} & & & \\
\hline \mathtt{16} & \mathtt{15} & \mathtt{14} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{17} & \mathtt{12} & \mathtt{07} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{34} & \mathtt{31} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{18} & \mathtt{06} & & & \\
\hline \mathtt{16} & \mathtt{15} & \mathtt{14} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{17} & \mathtt{12} & \mathtt{07} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{33} & \mathtt{32} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{18} & \mathtt{06} & & & \\
\hline \mathtt{16} & \mathtt{15} & \mathtt{14} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{17} & \mathtt{12} & \mathtt{07} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{39} & \mathtt{26} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{17} & \mathtt{11} & & & \\
\hline \mathtt{22} & \mathtt{15} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{38} & \mathtt{27} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{17} & \mathtt{11} & & & \\
\hline \mathtt{22} & \mathtt{15} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{17} & \mathtt{11} & & & \\
\hline \mathtt{22} & \mathtt{15} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{17} & \mathtt{11} & & & \\
\hline \mathtt{22} & \mathtt{15} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{17} & \mathtt{11} & & & \\
\hline \mathtt{22} & \mathtt{15} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{34} & \mathtt{31} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{17} & \mathtt{11} & & & \\
\hline \mathtt{22} & \mathtt{15} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{33} & \mathtt{32} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{17} & \mathtt{11} & & & \\
\hline \mathtt{22} & \mathtt{15} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{39} & \mathtt{26} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{38} & \mathtt{27} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{34} & \mathtt{31} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{33} & \mathtt{32} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{39} & \mathtt{26} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{38} & \mathtt{27} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{34} & \mathtt{31} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{33} & \mathtt{32} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{17} & \mathtt{15} & \mathtt{12} & & & \\
\hline \mathtt{20} & \mathtt{18} & \mathtt{11} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{39} & \mathtt{26} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{20} & \mathtt{17} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{38} & \mathtt{27} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{20} & \mathtt{17} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{20} & \mathtt{17} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{20} & \mathtt{17} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{20} & \mathtt{17} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{34} & \mathtt{31} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{20} & \mathtt{17} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{33} & \mathtt{32} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{20} & \mathtt{17} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{39} & \mathtt{26} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{17} & \mathtt{09} & & & \\
\hline \mathtt{20} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{38} & \mathtt{27} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{17} & \mathtt{09} & & & \\
\hline \mathtt{20} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{17} & \mathtt{09} & & & \\
\hline \mathtt{20} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{17} & \mathtt{09} & & & \\
\hline \mathtt{20} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{17} & \mathtt{09} & & & \\
\hline \mathtt{20} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{34} & \mathtt{31} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{17} & \mathtt{09} & & & \\
\hline \mathtt{20} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{33} & \mathtt{32} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{18} & \mathtt{17} & \mathtt{09} & & & \\
\hline \mathtt{20} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{39} & \mathtt{26} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{17} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{38} & \mathtt{27} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{17} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{17} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{17} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{17} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{34} & \mathtt{31} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{17} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{33} & \mathtt{32} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{17} & \mathtt{15} & \mathtt{11} & & & \\
\hline \mathtt{19} & \mathtt{18} & \mathtt{12} & \mathtt{09} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{39} & \mathtt{26} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{38} & \mathtt{27} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{34} & \mathtt{31} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{33} & \mathtt{32} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{39} & \mathtt{26} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{38} & \mathtt{27} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{34} & \mathtt{31} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{33} & \mathtt{32} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{15} & \mathtt{09} & & & \\
\hline \mathtt{18} & \mathtt{17} & \mathtt{12} & \mathtt{11} & \mathtt{07} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{39} & \mathtt{26} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{38} & \mathtt{27} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{34} & \mathtt{31} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{33} & \mathtt{32} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{22} & \mathtt{19} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{39} & \mathtt{26} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{38} & \mathtt{27} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{34} & \mathtt{31} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{33} & \mathtt{32} & & & & & \\
\hline \mathtt{24} & \mathtt{22} & \mathtt{19} & & & & \\
\hline \mathtt{21} & \mathtt{20} & \mathtt{17} & \mathtt{07} & & & \\
\hline \mathtt{18} & \mathtt{15} & \mathtt{12} & \mathtt{11} & \mathtt{09} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{14} & \mathtt{06} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{39} & \mathtt{26} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{17} & \mathtt{15} & \mathtt{14} & & & \\
\hline \mathtt{22} & \mathtt{18} & \mathtt{12} & \mathtt{07} & \mathtt{06} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{11} & \mathtt{09} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
$
$
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{38} & \mathtt{27} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{17} & \mathtt{15} & \mathtt{14} & & & \\
\hline \mathtt{22} & \mathtt{18} & \mathtt{12} & \mathtt{07} & \mathtt{06} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{11} & \mathtt{09} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{37} & \mathtt{28} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{17} & \mathtt{15} & \mathtt{14} & & & \\
\hline \mathtt{22} & \mathtt{18} & \mathtt{12} & \mathtt{07} & \mathtt{06} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{11} & \mathtt{09} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{36} & \mathtt{29} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{17} & \mathtt{15} & \mathtt{14} & & & \\
\hline \mathtt{22} & \mathtt{18} & \mathtt{12} & \mathtt{07} & \mathtt{06} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{11} & \mathtt{09} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\qquad
\begin{array}{|c|c|c|c|c|c|c|C} \hline \mathtt{65} & & & & & & \\
\hline \mathtt{35} & \mathtt{30} & & & & & \\
\hline \mathtt{24} & \mathtt{21} & \mathtt{20} & & & & \\
\hline \mathtt{19} & \mathtt{17} & \mathtt{15} & \mathtt{14} & & & \\
\hline \mathtt{22} & \mathtt{18} & \mathtt{12} & \mathtt{07} & \mathtt{06} & & \\
\hline \mathtt{23} & \mathtt{16} & \mathtt{11} & \mathtt{09} & \mathtt{04} & \mathtt{02} & \\
\hline \mathtt{25} & \mathtt{13} & \mathtt{10} & \mathtt{08} & \mathtt{05} & \mathtt{03} & \mathtt{01} \\\hline\end{array}
\\
\vdots$
il panurgo
Principio di Relatività: $\mathbb{m} \not \to \mathbb{M} \, \Longleftrightarrow \, \mathbb{M} \not \to \mathbb{m}$
"Se la montagna non va a Maometto, Maometto NON va alla montagna"
Principio di Relatività: $\mathbb{m} \not \to \mathbb{M} \, \Longleftrightarrow \, \mathbb{M} \not \to \mathbb{m}$
"Se la montagna non va a Maometto, Maometto NON va alla montagna"
Re: Scalinate di mattoni
Ottimo Panurgo! Ora, usando quanto detto da Gianfranco nel suo intervento del 7 aprile possiamo riassumere così:
n=2 Min(m)=3
n=3 Min(m)=8
n=4 Min(m)=15
n=5 Min(m)=27
n=6 Min(m)=43
n=7 Min(m)=65
n=2 Min(m)=3
n=3 Min(m)=8
n=4 Min(m)=15
n=5 Min(m)=27
n=6 Min(m)=43
n=7 Min(m)=65
Re: Scalinate di mattoni
Eccoli qui: A047837
(Bruno)
...........................
Invisibile un vento
l'ha apena sfioragia
sospension d'un momento;
e la bola iridessente gera 'ndagia.
{Biagio Marin}
................................................................
Meglio soluzioni sbagliate che risposte esatte.
{Rudi Mathematici}
...........................
Invisibile un vento
l'ha apena sfioragia
sospension d'un momento;
e la bola iridessente gera 'ndagia.
{Biagio Marin}
................................................................
Meglio soluzioni sbagliate che risposte esatte.
{Rudi Mathematici}
Re: Scalinate di mattoni
Non sapevo che il mio problema fosse già noto, io ho preso ispirazione da Base Cinque, dai mattoni numerati. Comunque, dopo il sonnellino postprandiale ho provato a esaminare il caso n=8 e ho trovato questa scalinata in cui ci sono i numeri da 1 a 33, poi 40, 64 e 95:
95
64 31
40 29 26
32 30 18 15
33 25 17 16 04
27 24 20 13 06 05
28 22 11 10 09 08 07
23 21 19 14 12 03 02 01
dall'oeis vedo che il minimo è 94, ci sono solo andato vicino…
95
64 31
40 29 26
32 30 18 15
33 25 17 16 04
27 24 20 13 06 05
28 22 11 10 09 08 07
23 21 19 14 12 03 02 01
dall'oeis vedo che il minimo è 94, ci sono solo andato vicino…
Re: Scalinate di mattoni
Una scala bella e agevole e ora infatti sappiamo che ne esistono da "94".
(Bruno)
...........................
Invisibile un vento
l'ha apena sfioragia
sospension d'un momento;
e la bola iridessente gera 'ndagia.
{Biagio Marin}
................................................................
Meglio soluzioni sbagliate che risposte esatte.
{Rudi Mathematici}
...........................
Invisibile un vento
l'ha apena sfioragia
sospension d'un momento;
e la bola iridessente gera 'ndagia.
{Biagio Marin}
................................................................
Meglio soluzioni sbagliate che risposte esatte.
{Rudi Mathematici}