Contare semplici sottinsiemi...

[Admin]

Trovare il numero dei sottinsiemi di $\left\{1, 2, 3, ..., 2000 \right\}$ la cui somma degli elementi è divisibile per $5$.

P.S.: la soluzione a questo problema mi ha lasciato esterrefatto.

[Quelo]

A occhio direi 1/5
I possibili sottoinsiemi sono nell'ordine di $10^{602}$ (per l'esattezza $2^{2000}-1$)
Con una tale quantità di numeri la differenza con 1/5 sarà infinitesimale

[Admin]

Va considerato anche l'insieme vuoto.
Siamo un bel pò distanti da $\frac{1}{5}$ .

[Quelo]

Ok, l'insieme vuoto mi era sfuggito, però è uno, non dovrebbe fare differenza.
Faccio un esempio con l'insieme (1,2,3,4,5,6,7,8,9,10), per vedere se ho capito il problema

I sottoinsiemi sono i seguenti?

Codice: Seleziona tutto

∑()=0
∑(1,)=1
∑(2,)=2
∑(3,)=3
∑(4,)=4
∑(5,)=5
∑(6,)=6
∑(7,)=7
∑(8,)=8
∑(9,)=9
∑(10,)=10
∑(1, 2)=3
∑(1, 3)=4
∑(1, 4)=5
∑(1, 5)=6
∑(1, 6)=7
∑(1, 7)=8
∑(1, 8)=9
∑(1, 9)=10
∑(1, 10)=11
∑(2, 3)=5
∑(2, 4)=6
∑(2, 5)=7
∑(2, 6)=8
∑(2, 7)=9
∑(2, 8)=10
∑(2, 9)=11
∑(2, 10)=12
∑(3, 4)=7
∑(3, 5)=8
∑(3, 6)=9
∑(3, 7)=10
∑(3, 8)=11
∑(3, 9)=12
∑(3, 10)=13
∑(4, 5)=9
∑(4, 6)=10
∑(4, 7)=11
∑(4, 8)=12
∑(4, 9)=13
∑(4, 10)=14
∑(5, 6)=11
∑(5, 7)=12
∑(5, 8)=13
∑(5, 9)=14
∑(5, 10)=15
∑(6, 7)=13
∑(6, 8)=14
∑(6, 9)=15
∑(6, 10)=16
∑(7, 8)=15
∑(7, 9)=16
∑(7, 10)=17
∑(8, 9)=17
∑(8, 10)=18
∑(9, 10)=19
∑(1, 2, 3)=6
∑(1, 2, 4)=7
∑(1, 2, 5)=8
∑(1, 2, 6)=9
∑(1, 2, 7)=10
∑(1, 2, 8)=11
∑(1, 2, 9)=12
∑(1, 2, 10)=13
∑(1, 3, 4)=8
∑(1, 3, 5)=9
∑(1, 3, 6)=10
∑(1, 3, 7)=11
∑(1, 3, 8)=12
∑(1, 3, 9)=13
∑(1, 3, 10)=14
∑(1, 4, 5)=10
∑(1, 4, 6)=11
∑(1, 4, 7)=12
∑(1, 4, 8)=13
∑(1, 4, 9)=14
∑(1, 4, 10)=15
∑(1, 5, 6)=12
∑(1, 5, 7)=13
∑(1, 5, 8)=14
∑(1, 5, 9)=15
∑(1, 5, 10)=16
∑(1, 6, 7)=14
∑(1, 6, 8)=15
∑(1, 6, 9)=16
∑(1, 6, 10)=17
∑(1, 7, 8)=16
∑(1, 7, 9)=17
∑(1, 7, 10)=18
∑(1, 8, 9)=18
∑(1, 8, 10)=19
∑(1, 9, 10)=20
∑(2, 3, 4)=9
∑(2, 3, 5)=10
∑(2, 3, 6)=11
∑(2, 3, 7)=12
∑(2, 3, 8)=13
∑(2, 3, 9)=14
∑(2, 3, 10)=15
∑(2, 4, 5)=11
∑(2, 4, 6)=12
∑(2, 4, 7)=13
∑(2, 4, 8)=14
∑(2, 4, 9)=15
∑(2, 4, 10)=16
∑(2, 5, 6)=13
∑(2, 5, 7)=14
∑(2, 5, 8)=15
∑(2, 5, 9)=16
∑(2, 5, 10)=17
∑(2, 6, 7)=15
∑(2, 6, 8)=16
∑(2, 6, 9)=17
∑(2, 6, 10)=18
∑(2, 7, 8)=17
∑(2, 7, 9)=18
∑(2, 7, 10)=19
∑(2, 8, 9)=19
∑(2, 8, 10)=20
∑(2, 9, 10)=21
∑(3, 4, 5)=12
∑(3, 4, 6)=13
∑(3, 4, 7)=14
∑(3, 4, 8)=15
∑(3, 4, 9)=16
∑(3, 4, 10)=17
∑(3, 5, 6)=14
∑(3, 5, 7)=15
∑(3, 5, 8)=16
∑(3, 5, 9)=17
∑(3, 5, 10)=18
∑(3, 6, 7)=16
∑(3, 6, 8)=17
∑(3, 6, 9)=18
∑(3, 6, 10)=19
∑(3, 7, 8)=18
∑(3, 7, 9)=19
∑(3, 7, 10)=20
∑(3, 8, 9)=20
∑(3, 8, 10)=21
∑(3, 9, 10)=22
∑(4, 5, 6)=15
∑(4, 5, 7)=16
∑(4, 5, 8)=17
∑(4, 5, 9)=18
∑(4, 5, 10)=19
∑(4, 6, 7)=17
∑(4, 6, 8)=18
∑(4, 6, 9)=19
∑(4, 6, 10)=20
∑(4, 7, 8)=19
∑(4, 7, 9)=20
∑(4, 7, 10)=21
∑(4, 8, 9)=21
∑(4, 8, 10)=22
∑(4, 9, 10)=23
∑(5, 6, 7)=18
∑(5, 6, 8)=19
∑(5, 6, 9)=20
∑(5, 6, 10)=21
∑(5, 7, 8)=20
∑(5, 7, 9)=21
∑(5, 7, 10)=22
∑(5, 8, 9)=22
∑(5, 8, 10)=23
∑(5, 9, 10)=24
∑(6, 7, 8)=21
∑(6, 7, 9)=22
∑(6, 7, 10)=23
∑(6, 8, 9)=23
∑(6, 8, 10)=24
∑(6, 9, 10)=25
∑(7, 8, 9)=24
∑(7, 8, 10)=25
∑(7, 9, 10)=26
∑(8, 9, 10)=27
∑(1, 2, 3, 4)=10
∑(1, 2, 3, 5)=11
∑(1, 2, 3, 6)=12
∑(1, 2, 3, 7)=13
∑(1, 2, 3, 8)=14
∑(1, 2, 3, 9)=15
∑(1, 2, 3, 10)=16
∑(1, 2, 4, 5)=12
∑(1, 2, 4, 6)=13
∑(1, 2, 4, 7)=14
∑(1, 2, 4, 8)=15
∑(1, 2, 4, 9)=16
∑(1, 2, 4, 10)=17
∑(1, 2, 5, 6)=14
∑(1, 2, 5, 7)=15
∑(1, 2, 5, 8)=16
∑(1, 2, 5, 9)=17
∑(1, 2, 5, 10)=18
∑(1, 2, 6, 7)=16
∑(1, 2, 6, 8)=17
∑(1, 2, 6, 9)=18
∑(1, 2, 6, 10)=19
∑(1, 2, 7, 8)=18
∑(1, 2, 7, 9)=19
∑(1, 2, 7, 10)=20
∑(1, 2, 8, 9)=20
∑(1, 2, 8, 10)=21
∑(1, 2, 9, 10)=22
∑(1, 3, 4, 5)=13
∑(1, 3, 4, 6)=14
∑(1, 3, 4, 7)=15
∑(1, 3, 4, 8)=16
∑(1, 3, 4, 9)=17
∑(1, 3, 4, 10)=18
∑(1, 3, 5, 6)=15
∑(1, 3, 5, 7)=16
∑(1, 3, 5, 8)=17
∑(1, 3, 5, 9)=18
∑(1, 3, 5, 10)=19
∑(1, 3, 6, 7)=17
∑(1, 3, 6, 8)=18
∑(1, 3, 6, 9)=19
∑(1, 3, 6, 10)=20
∑(1, 3, 7, 8)=19
∑(1, 3, 7, 9)=20
∑(1, 3, 7, 10)=21
∑(1, 3, 8, 9)=21
∑(1, 3, 8, 10)=22
∑(1, 3, 9, 10)=23
∑(1, 4, 5, 6)=16
∑(1, 4, 5, 7)=17
∑(1, 4, 5, 8)=18
∑(1, 4, 5, 9)=19
∑(1, 4, 5, 10)=20
∑(1, 4, 6, 7)=18
∑(1, 4, 6, 8)=19
∑(1, 4, 6, 9)=20
∑(1, 4, 6, 10)=21
∑(1, 4, 7, 8)=20
∑(1, 4, 7, 9)=21
∑(1, 4, 7, 10)=22
∑(1, 4, 8, 9)=22
∑(1, 4, 8, 10)=23
∑(1, 4, 9, 10)=24
∑(1, 5, 6, 7)=19
∑(1, 5, 6, 8)=20
∑(1, 5, 6, 9)=21
∑(1, 5, 6, 10)=22
∑(1, 5, 7, 8)=21
∑(1, 5, 7, 9)=22
∑(1, 5, 7, 10)=23
∑(1, 5, 8, 9)=23
∑(1, 5, 8, 10)=24
∑(1, 5, 9, 10)=25
∑(1, 6, 7, 8)=22
∑(1, 6, 7, 9)=23
∑(1, 6, 7, 10)=24
∑(1, 6, 8, 9)=24
∑(1, 6, 8, 10)=25
∑(1, 6, 9, 10)=26
∑(1, 7, 8, 9)=25
∑(1, 7, 8, 10)=26
∑(1, 7, 9, 10)=27
∑(1, 8, 9, 10)=28
∑(2, 3, 4, 5)=14
∑(2, 3, 4, 6)=15
∑(2, 3, 4, 7)=16
∑(2, 3, 4, 8)=17
∑(2, 3, 4, 9)=18
∑(2, 3, 4, 10)=19
∑(2, 3, 5, 6)=16
∑(2, 3, 5, 7)=17
∑(2, 3, 5, 8)=18
∑(2, 3, 5, 9)=19
∑(2, 3, 5, 10)=20
∑(2, 3, 6, 7)=18
∑(2, 3, 6, 8)=19
∑(2, 3, 6, 9)=20
∑(2, 3, 6, 10)=21
∑(2, 3, 7, 8)=20
∑(2, 3, 7, 9)=21
∑(2, 3, 7, 10)=22
∑(2, 3, 8, 9)=22
∑(2, 3, 8, 10)=23
∑(2, 3, 9, 10)=24
∑(2, 4, 5, 6)=17
∑(2, 4, 5, 7)=18
∑(2, 4, 5, 8)=19
∑(2, 4, 5, 9)=20
∑(2, 4, 5, 10)=21
∑(2, 4, 6, 7)=19
∑(2, 4, 6, 8)=20
∑(2, 4, 6, 9)=21
∑(2, 4, 6, 10)=22
∑(2, 4, 7, 8)=21
∑(2, 4, 7, 9)=22
∑(2, 4, 7, 10)=23
∑(2, 4, 8, 9)=23
∑(2, 4, 8, 10)=24
∑(2, 4, 9, 10)=25
∑(2, 5, 6, 7)=20
∑(2, 5, 6, 8)=21
∑(2, 5, 6, 9)=22
∑(2, 5, 6, 10)=23
∑(2, 5, 7, 8)=22
∑(2, 5, 7, 9)=23
∑(2, 5, 7, 10)=24
∑(2, 5, 8, 9)=24
∑(2, 5, 8, 10)=25
∑(2, 5, 9, 10)=26
∑(2, 6, 7, 8)=23
∑(2, 6, 7, 9)=24
∑(2, 6, 7, 10)=25
∑(2, 6, 8, 9)=25
∑(2, 6, 8, 10)=26
∑(2, 6, 9, 10)=27
∑(2, 7, 8, 9)=26
∑(2, 7, 8, 10)=27
∑(2, 7, 9, 10)=28
∑(2, 8, 9, 10)=29
∑(3, 4, 5, 6)=18
∑(3, 4, 5, 7)=19
∑(3, 4, 5, 8)=20
∑(3, 4, 5, 9)=21
∑(3, 4, 5, 10)=22
∑(3, 4, 6, 7)=20
∑(3, 4, 6, 8)=21
∑(3, 4, 6, 9)=22
∑(3, 4, 6, 10)=23
∑(3, 4, 7, 8)=22
∑(3, 4, 7, 9)=23
∑(3, 4, 7, 10)=24
∑(3, 4, 8, 9)=24
∑(3, 4, 8, 10)=25
∑(3, 4, 9, 10)=26
∑(3, 5, 6, 7)=21
∑(3, 5, 6, 8)=22
∑(3, 5, 6, 9)=23
∑(3, 5, 6, 10)=24
∑(3, 5, 7, 8)=23
∑(3, 5, 7, 9)=24
∑(3, 5, 7, 10)=25
∑(3, 5, 8, 9)=25
∑(3, 5, 8, 10)=26
∑(3, 5, 9, 10)=27
∑(3, 6, 7, 8)=24
∑(3, 6, 7, 9)=25
∑(3, 6, 7, 10)=26
∑(3, 6, 8, 9)=26
∑(3, 6, 8, 10)=27
∑(3, 6, 9, 10)=28
∑(3, 7, 8, 9)=27
∑(3, 7, 8, 10)=28
∑(3, 7, 9, 10)=29
∑(3, 8, 9, 10)=30
∑(4, 5, 6, 7)=22
∑(4, 5, 6, 8)=23
∑(4, 5, 6, 9)=24
∑(4, 5, 6, 10)=25
∑(4, 5, 7, 8)=24
∑(4, 5, 7, 9)=25
∑(4, 5, 7, 10)=26
∑(4, 5, 8, 9)=26
∑(4, 5, 8, 10)=27
∑(4, 5, 9, 10)=28
∑(4, 6, 7, 8)=25
∑(4, 6, 7, 9)=26
∑(4, 6, 7, 10)=27
∑(4, 6, 8, 9)=27
∑(4, 6, 8, 10)=28
∑(4, 6, 9, 10)=29
∑(4, 7, 8, 9)=28
∑(4, 7, 8, 10)=29
∑(4, 7, 9, 10)=30
∑(4, 8, 9, 10)=31
∑(5, 6, 7, 8)=26
∑(5, 6, 7, 9)=27
∑(5, 6, 7, 10)=28
∑(5, 6, 8, 9)=28
∑(5, 6, 8, 10)=29
∑(5, 6, 9, 10)=30
∑(5, 7, 8, 9)=29
∑(5, 7, 8, 10)=30
∑(5, 7, 9, 10)=31
∑(5, 8, 9, 10)=32
∑(6, 7, 8, 9)=30
∑(6, 7, 8, 10)=31
∑(6, 7, 9, 10)=32
∑(6, 8, 9, 10)=33
∑(7, 8, 9, 10)=34
∑(1, 2, 3, 4, 5)=15
∑(1, 2, 3, 4, 6)=16
∑(1, 2, 3, 4, 7)=17
∑(1, 2, 3, 4, 8)=18
∑(1, 2, 3, 4, 9)=19
∑(1, 2, 3, 4, 10)=20
∑(1, 2, 3, 5, 6)=17
∑(1, 2, 3, 5, 7)=18
∑(1, 2, 3, 5, 8)=19
∑(1, 2, 3, 5, 9)=20
∑(1, 2, 3, 5, 10)=21
∑(1, 2, 3, 6, 7)=19
∑(1, 2, 3, 6, 8)=20
∑(1, 2, 3, 6, 9)=21
∑(1, 2, 3, 6, 10)=22
∑(1, 2, 3, 7, 8)=21
∑(1, 2, 3, 7, 9)=22
∑(1, 2, 3, 7, 10)=23
∑(1, 2, 3, 8, 9)=23
∑(1, 2, 3, 8, 10)=24
∑(1, 2, 3, 9, 10)=25
∑(1, 2, 4, 5, 6)=18
∑(1, 2, 4, 5, 7)=19
∑(1, 2, 4, 5, 8)=20
∑(1, 2, 4, 5, 9)=21
∑(1, 2, 4, 5, 10)=22
∑(1, 2, 4, 6, 7)=20
∑(1, 2, 4, 6, 8)=21
∑(1, 2, 4, 6, 9)=22
∑(1, 2, 4, 6, 10)=23
∑(1, 2, 4, 7, 8)=22
∑(1, 2, 4, 7, 9)=23
∑(1, 2, 4, 7, 10)=24
∑(1, 2, 4, 8, 9)=24
∑(1, 2, 4, 8, 10)=25
∑(1, 2, 4, 9, 10)=26
∑(1, 2, 5, 6, 7)=21
∑(1, 2, 5, 6, 8)=22
∑(1, 2, 5, 6, 9)=23
∑(1, 2, 5, 6, 10)=24
∑(1, 2, 5, 7, 8)=23
∑(1, 2, 5, 7, 9)=24
∑(1, 2, 5, 7, 10)=25
∑(1, 2, 5, 8, 9)=25
∑(1, 2, 5, 8, 10)=26
∑(1, 2, 5, 9, 10)=27
∑(1, 2, 6, 7, 8)=24
∑(1, 2, 6, 7, 9)=25
∑(1, 2, 6, 7, 10)=26
∑(1, 2, 6, 8, 9)=26
∑(1, 2, 6, 8, 10)=27
∑(1, 2, 6, 9, 10)=28
∑(1, 2, 7, 8, 9)=27
∑(1, 2, 7, 8, 10)=28
∑(1, 2, 7, 9, 10)=29
∑(1, 2, 8, 9, 10)=30
∑(1, 3, 4, 5, 6)=19
∑(1, 3, 4, 5, 7)=20
∑(1, 3, 4, 5, 8)=21
∑(1, 3, 4, 5, 9)=22
∑(1, 3, 4, 5, 10)=23
∑(1, 3, 4, 6, 7)=21
∑(1, 3, 4, 6, 8)=22
∑(1, 3, 4, 6, 9)=23
∑(1, 3, 4, 6, 10)=24
∑(1, 3, 4, 7, 8)=23
∑(1, 3, 4, 7, 9)=24
∑(1, 3, 4, 7, 10)=25
∑(1, 3, 4, 8, 9)=25
∑(1, 3, 4, 8, 10)=26
∑(1, 3, 4, 9, 10)=27
∑(1, 3, 5, 6, 7)=22
∑(1, 3, 5, 6, 8)=23
∑(1, 3, 5, 6, 9)=24
∑(1, 3, 5, 6, 10)=25
∑(1, 3, 5, 7, 8)=24
∑(1, 3, 5, 7, 9)=25
∑(1, 3, 5, 7, 10)=26
∑(1, 3, 5, 8, 9)=26
∑(1, 3, 5, 8, 10)=27
∑(1, 3, 5, 9, 10)=28
∑(1, 3, 6, 7, 8)=25
∑(1, 3, 6, 7, 9)=26
∑(1, 3, 6, 7, 10)=27
∑(1, 3, 6, 8, 9)=27
∑(1, 3, 6, 8, 10)=28
∑(1, 3, 6, 9, 10)=29
∑(1, 3, 7, 8, 9)=28
∑(1, 3, 7, 8, 10)=29
∑(1, 3, 7, 9, 10)=30
∑(1, 3, 8, 9, 10)=31
∑(1, 4, 5, 6, 7)=23
∑(1, 4, 5, 6, 8)=24
∑(1, 4, 5, 6, 9)=25
∑(1, 4, 5, 6, 10)=26
∑(1, 4, 5, 7, 8)=25
∑(1, 4, 5, 7, 9)=26
∑(1, 4, 5, 7, 10)=27
∑(1, 4, 5, 8, 9)=27
∑(1, 4, 5, 8, 10)=28
∑(1, 4, 5, 9, 10)=29
∑(1, 4, 6, 7, 8)=26
∑(1, 4, 6, 7, 9)=27
∑(1, 4, 6, 7, 10)=28
∑(1, 4, 6, 8, 9)=28
∑(1, 4, 6, 8, 10)=29
∑(1, 4, 6, 9, 10)=30
∑(1, 4, 7, 8, 9)=29
∑(1, 4, 7, 8, 10)=30
∑(1, 4, 7, 9, 10)=31
∑(1, 4, 8, 9, 10)=32
∑(1, 5, 6, 7, 8)=27
∑(1, 5, 6, 7, 9)=28
∑(1, 5, 6, 7, 10)=29
∑(1, 5, 6, 8, 9)=29
∑(1, 5, 6, 8, 10)=30
∑(1, 5, 6, 9, 10)=31
∑(1, 5, 7, 8, 9)=30
∑(1, 5, 7, 8, 10)=31
∑(1, 5, 7, 9, 10)=32
∑(1, 5, 8, 9, 10)=33
∑(1, 6, 7, 8, 9)=31
∑(1, 6, 7, 8, 10)=32
∑(1, 6, 7, 9, 10)=33
∑(1, 6, 8, 9, 10)=34
∑(1, 7, 8, 9, 10)=35
∑(2, 3, 4, 5, 6)=20
∑(2, 3, 4, 5, 7)=21
∑(2, 3, 4, 5, 8)=22
∑(2, 3, 4, 5, 9)=23
∑(2, 3, 4, 5, 10)=24
∑(2, 3, 4, 6, 7)=22
∑(2, 3, 4, 6, 8)=23
∑(2, 3, 4, 6, 9)=24
∑(2, 3, 4, 6, 10)=25
∑(2, 3, 4, 7, 8)=24
∑(2, 3, 4, 7, 9)=25
∑(2, 3, 4, 7, 10)=26
∑(2, 3, 4, 8, 9)=26
∑(2, 3, 4, 8, 10)=27
∑(2, 3, 4, 9, 10)=28
∑(2, 3, 5, 6, 7)=23
∑(2, 3, 5, 6, 8)=24
∑(2, 3, 5, 6, 9)=25
∑(2, 3, 5, 6, 10)=26
∑(2, 3, 5, 7, 8)=25
∑(2, 3, 5, 7, 9)=26
∑(2, 3, 5, 7, 10)=27
∑(2, 3, 5, 8, 9)=27
∑(2, 3, 5, 8, 10)=28
∑(2, 3, 5, 9, 10)=29
∑(2, 3, 6, 7, 8)=26
∑(2, 3, 6, 7, 9)=27
∑(2, 3, 6, 7, 10)=28
∑(2, 3, 6, 8, 9)=28
∑(2, 3, 6, 8, 10)=29
∑(2, 3, 6, 9, 10)=30
∑(2, 3, 7, 8, 9)=29
∑(2, 3, 7, 8, 10)=30
∑(2, 3, 7, 9, 10)=31
∑(2, 3, 8, 9, 10)=32
∑(2, 4, 5, 6, 7)=24
∑(2, 4, 5, 6, 8)=25
∑(2, 4, 5, 6, 9)=26
∑(2, 4, 5, 6, 10)=27
∑(2, 4, 5, 7, 8)=26
∑(2, 4, 5, 7, 9)=27
∑(2, 4, 5, 7, 10)=28
∑(2, 4, 5, 8, 9)=28
∑(2, 4, 5, 8, 10)=29
∑(2, 4, 5, 9, 10)=30
∑(2, 4, 6, 7, 8)=27
∑(2, 4, 6, 7, 9)=28
∑(2, 4, 6, 7, 10)=29
∑(2, 4, 6, 8, 9)=29
∑(2, 4, 6, 8, 10)=30
∑(2, 4, 6, 9, 10)=31
∑(2, 4, 7, 8, 9)=30
∑(2, 4, 7, 8, 10)=31
∑(2, 4, 7, 9, 10)=32
∑(2, 4, 8, 9, 10)=33
∑(2, 5, 6, 7, 8)=28
∑(2, 5, 6, 7, 9)=29
∑(2, 5, 6, 7, 10)=30
∑(2, 5, 6, 8, 9)=30
∑(2, 5, 6, 8, 10)=31
∑(2, 5, 6, 9, 10)=32
∑(2, 5, 7, 8, 9)=31
∑(2, 5, 7, 8, 10)=32
∑(2, 5, 7, 9, 10)=33
∑(2, 5, 8, 9, 10)=34
∑(2, 6, 7, 8, 9)=32
∑(2, 6, 7, 8, 10)=33
∑(2, 6, 7, 9, 10)=34
∑(2, 6, 8, 9, 10)=35
∑(2, 7, 8, 9, 10)=36
∑(3, 4, 5, 6, 7)=25
∑(3, 4, 5, 6, 8)=26
∑(3, 4, 5, 6, 9)=27
∑(3, 4, 5, 6, 10)=28
∑(3, 4, 5, 7, 8)=27
∑(3, 4, 5, 7, 9)=28
∑(3, 4, 5, 7, 10)=29
∑(3, 4, 5, 8, 9)=29
∑(3, 4, 5, 8, 10)=30
∑(3, 4, 5, 9, 10)=31
∑(3, 4, 6, 7, 8)=28
∑(3, 4, 6, 7, 9)=29
∑(3, 4, 6, 7, 10)=30
∑(3, 4, 6, 8, 9)=30
∑(3, 4, 6, 8, 10)=31
∑(3, 4, 6, 9, 10)=32
∑(3, 4, 7, 8, 9)=31
∑(3, 4, 7, 8, 10)=32
∑(3, 4, 7, 9, 10)=33
∑(3, 4, 8, 9, 10)=34
∑(3, 5, 6, 7, 8)=29
∑(3, 5, 6, 7, 9)=30
∑(3, 5, 6, 7, 10)=31
∑(3, 5, 6, 8, 9)=31
∑(3, 5, 6, 8, 10)=32
∑(3, 5, 6, 9, 10)=33
∑(3, 5, 7, 8, 9)=32
∑(3, 5, 7, 8, 10)=33
∑(3, 5, 7, 9, 10)=34
∑(3, 5, 8, 9, 10)=35
∑(3, 6, 7, 8, 9)=33
∑(3, 6, 7, 8, 10)=34
∑(3, 6, 7, 9, 10)=35
∑(3, 6, 8, 9, 10)=36
∑(3, 7, 8, 9, 10)=37
∑(4, 5, 6, 7, 8)=30
∑(4, 5, 6, 7, 9)=31
∑(4, 5, 6, 7, 10)=32
∑(4, 5, 6, 8, 9)=32
∑(4, 5, 6, 8, 10)=33
∑(4, 5, 6, 9, 10)=34
∑(4, 5, 7, 8, 9)=33
∑(4, 5, 7, 8, 10)=34
∑(4, 5, 7, 9, 10)=35
∑(4, 5, 8, 9, 10)=36
∑(4, 6, 7, 8, 9)=34
∑(4, 6, 7, 8, 10)=35
∑(4, 6, 7, 9, 10)=36
∑(4, 6, 8, 9, 10)=37
∑(4, 7, 8, 9, 10)=38
∑(5, 6, 7, 8, 9)=35
∑(5, 6, 7, 8, 10)=36
∑(5, 6, 7, 9, 10)=37
∑(5, 6, 8, 9, 10)=38
∑(5, 7, 8, 9, 10)=39
∑(6, 7, 8, 9, 10)=40
∑(1, 2, 3, 4, 5, 6)=21
∑(1, 2, 3, 4, 5, 7)=22
∑(1, 2, 3, 4, 5, 8)=23
∑(1, 2, 3, 4, 5, 9)=24
∑(1, 2, 3, 4, 5, 10)=25
∑(1, 2, 3, 4, 6, 7)=23
∑(1, 2, 3, 4, 6, 8)=24
∑(1, 2, 3, 4, 6, 9)=25
∑(1, 2, 3, 4, 6, 10)=26
∑(1, 2, 3, 4, 7, 8)=25
∑(1, 2, 3, 4, 7, 9)=26
∑(1, 2, 3, 4, 7, 10)=27
∑(1, 2, 3, 4, 8, 9)=27
∑(1, 2, 3, 4, 8, 10)=28
∑(1, 2, 3, 4, 9, 10)=29
∑(1, 2, 3, 5, 6, 7)=24
∑(1, 2, 3, 5, 6, 8)=25
∑(1, 2, 3, 5, 6, 9)=26
∑(1, 2, 3, 5, 6, 10)=27
∑(1, 2, 3, 5, 7, 8)=26
∑(1, 2, 3, 5, 7, 9)=27
∑(1, 2, 3, 5, 7, 10)=28
∑(1, 2, 3, 5, 8, 9)=28
∑(1, 2, 3, 5, 8, 10)=29
∑(1, 2, 3, 5, 9, 10)=30
∑(1, 2, 3, 6, 7, 8)=27
∑(1, 2, 3, 6, 7, 9)=28
∑(1, 2, 3, 6, 7, 10)=29
∑(1, 2, 3, 6, 8, 9)=29
∑(1, 2, 3, 6, 8, 10)=30
∑(1, 2, 3, 6, 9, 10)=31
∑(1, 2, 3, 7, 8, 9)=30
∑(1, 2, 3, 7, 8, 10)=31
∑(1, 2, 3, 7, 9, 10)=32
∑(1, 2, 3, 8, 9, 10)=33
∑(1, 2, 4, 5, 6, 7)=25
∑(1, 2, 4, 5, 6, 8)=26
∑(1, 2, 4, 5, 6, 9)=27
∑(1, 2, 4, 5, 6, 10)=28
∑(1, 2, 4, 5, 7, 8)=27
∑(1, 2, 4, 5, 7, 9)=28
∑(1, 2, 4, 5, 7, 10)=29
∑(1, 2, 4, 5, 8, 9)=29
∑(1, 2, 4, 5, 8, 10)=30
∑(1, 2, 4, 5, 9, 10)=31
∑(1, 2, 4, 6, 7, 8)=28
∑(1, 2, 4, 6, 7, 9)=29
∑(1, 2, 4, 6, 7, 10)=30
∑(1, 2, 4, 6, 8, 9)=30
∑(1, 2, 4, 6, 8, 10)=31
∑(1, 2, 4, 6, 9, 10)=32
∑(1, 2, 4, 7, 8, 9)=31
∑(1, 2, 4, 7, 8, 10)=32
∑(1, 2, 4, 7, 9, 10)=33
∑(1, 2, 4, 8, 9, 10)=34
∑(1, 2, 5, 6, 7, 8)=29
∑(1, 2, 5, 6, 7, 9)=30
∑(1, 2, 5, 6, 7, 10)=31
∑(1, 2, 5, 6, 8, 9)=31
∑(1, 2, 5, 6, 8, 10)=32
∑(1, 2, 5, 6, 9, 10)=33
∑(1, 2, 5, 7, 8, 9)=32
∑(1, 2, 5, 7, 8, 10)=33
∑(1, 2, 5, 7, 9, 10)=34
∑(1, 2, 5, 8, 9, 10)=35
∑(1, 2, 6, 7, 8, 9)=33
∑(1, 2, 6, 7, 8, 10)=34
∑(1, 2, 6, 7, 9, 10)=35
∑(1, 2, 6, 8, 9, 10)=36
∑(1, 2, 7, 8, 9, 10)=37
∑(1, 3, 4, 5, 6, 7)=26
∑(1, 3, 4, 5, 6, 8)=27
∑(1, 3, 4, 5, 6, 9)=28
∑(1, 3, 4, 5, 6, 10)=29
∑(1, 3, 4, 5, 7, 8)=28
∑(1, 3, 4, 5, 7, 9)=29
∑(1, 3, 4, 5, 7, 10)=30
∑(1, 3, 4, 5, 8, 9)=30
∑(1, 3, 4, 5, 8, 10)=31
∑(1, 3, 4, 5, 9, 10)=32
∑(1, 3, 4, 6, 7, 8)=29
∑(1, 3, 4, 6, 7, 9)=30
∑(1, 3, 4, 6, 7, 10)=31
∑(1, 3, 4, 6, 8, 9)=31
∑(1, 3, 4, 6, 8, 10)=32
∑(1, 3, 4, 6, 9, 10)=33
∑(1, 3, 4, 7, 8, 9)=32
∑(1, 3, 4, 7, 8, 10)=33
∑(1, 3, 4, 7, 9, 10)=34
∑(1, 3, 4, 8, 9, 10)=35
∑(1, 3, 5, 6, 7, 8)=30
∑(1, 3, 5, 6, 7, 9)=31
∑(1, 3, 5, 6, 7, 10)=32
∑(1, 3, 5, 6, 8, 9)=32
∑(1, 3, 5, 6, 8, 10)=33
∑(1, 3, 5, 6, 9, 10)=34
∑(1, 3, 5, 7, 8, 9)=33
∑(1, 3, 5, 7, 8, 10)=34
∑(1, 3, 5, 7, 9, 10)=35
∑(1, 3, 5, 8, 9, 10)=36
∑(1, 3, 6, 7, 8, 9)=34
∑(1, 3, 6, 7, 8, 10)=35
∑(1, 3, 6, 7, 9, 10)=36
∑(1, 3, 6, 8, 9, 10)=37
∑(1, 3, 7, 8, 9, 10)=38
∑(1, 4, 5, 6, 7, 8)=31
∑(1, 4, 5, 6, 7, 9)=32
∑(1, 4, 5, 6, 7, 10)=33
∑(1, 4, 5, 6, 8, 9)=33
∑(1, 4, 5, 6, 8, 10)=34
∑(1, 4, 5, 6, 9, 10)=35
∑(1, 4, 5, 7, 8, 9)=34
∑(1, 4, 5, 7, 8, 10)=35
∑(1, 4, 5, 7, 9, 10)=36
∑(1, 4, 5, 8, 9, 10)=37
∑(1, 4, 6, 7, 8, 9)=35
∑(1, 4, 6, 7, 8, 10)=36
∑(1, 4, 6, 7, 9, 10)=37
∑(1, 4, 6, 8, 9, 10)=38
∑(1, 4, 7, 8, 9, 10)=39
∑(1, 5, 6, 7, 8, 9)=36
∑(1, 5, 6, 7, 8, 10)=37
∑(1, 5, 6, 7, 9, 10)=38
∑(1, 5, 6, 8, 9, 10)=39
∑(1, 5, 7, 8, 9, 10)=40
∑(1, 6, 7, 8, 9, 10)=41
∑(2, 3, 4, 5, 6, 7)=27
∑(2, 3, 4, 5, 6, 8)=28
∑(2, 3, 4, 5, 6, 9)=29
∑(2, 3, 4, 5, 6, 10)=30
∑(2, 3, 4, 5, 7, 8)=29
∑(2, 3, 4, 5, 7, 9)=30
∑(2, 3, 4, 5, 7, 10)=31
∑(2, 3, 4, 5, 8, 9)=31
∑(2, 3, 4, 5, 8, 10)=32
∑(2, 3, 4, 5, 9, 10)=33
∑(2, 3, 4, 6, 7, 8)=30
∑(2, 3, 4, 6, 7, 9)=31
∑(2, 3, 4, 6, 7, 10)=32
∑(2, 3, 4, 6, 8, 9)=32
∑(2, 3, 4, 6, 8, 10)=33
∑(2, 3, 4, 6, 9, 10)=34
∑(2, 3, 4, 7, 8, 9)=33
∑(2, 3, 4, 7, 8, 10)=34
∑(2, 3, 4, 7, 9, 10)=35
∑(2, 3, 4, 8, 9, 10)=36
∑(2, 3, 5, 6, 7, 8)=31
∑(2, 3, 5, 6, 7, 9)=32
∑(2, 3, 5, 6, 7, 10)=33
∑(2, 3, 5, 6, 8, 9)=33
∑(2, 3, 5, 6, 8, 10)=34
∑(2, 3, 5, 6, 9, 10)=35
∑(2, 3, 5, 7, 8, 9)=34
∑(2, 3, 5, 7, 8, 10)=35
∑(2, 3, 5, 7, 9, 10)=36
∑(2, 3, 5, 8, 9, 10)=37
∑(2, 3, 6, 7, 8, 9)=35
∑(2, 3, 6, 7, 8, 10)=36
∑(2, 3, 6, 7, 9, 10)=37
∑(2, 3, 6, 8, 9, 10)=38
∑(2, 3, 7, 8, 9, 10)=39
∑(2, 4, 5, 6, 7, 8)=32
∑(2, 4, 5, 6, 7, 9)=33
∑(2, 4, 5, 6, 7, 10)=34
∑(2, 4, 5, 6, 8, 9)=34
∑(2, 4, 5, 6, 8, 10)=35
∑(2, 4, 5, 6, 9, 10)=36
∑(2, 4, 5, 7, 8, 9)=35
∑(2, 4, 5, 7, 8, 10)=36
∑(2, 4, 5, 7, 9, 10)=37
∑(2, 4, 5, 8, 9, 10)=38
∑(2, 4, 6, 7, 8, 9)=36
∑(2, 4, 6, 7, 8, 10)=37
∑(2, 4, 6, 7, 9, 10)=38
∑(2, 4, 6, 8, 9, 10)=39
∑(2, 4, 7, 8, 9, 10)=40
∑(2, 5, 6, 7, 8, 9)=37
∑(2, 5, 6, 7, 8, 10)=38
∑(2, 5, 6, 7, 9, 10)=39
∑(2, 5, 6, 8, 9, 10)=40
∑(2, 5, 7, 8, 9, 10)=41
∑(2, 6, 7, 8, 9, 10)=42
∑(3, 4, 5, 6, 7, 8)=33
∑(3, 4, 5, 6, 7, 9)=34
∑(3, 4, 5, 6, 7, 10)=35
∑(3, 4, 5, 6, 8, 9)=35
∑(3, 4, 5, 6, 8, 10)=36
∑(3, 4, 5, 6, 9, 10)=37
∑(3, 4, 5, 7, 8, 9)=36
∑(3, 4, 5, 7, 8, 10)=37
∑(3, 4, 5, 7, 9, 10)=38
∑(3, 4, 5, 8, 9, 10)=39
∑(3, 4, 6, 7, 8, 9)=37
∑(3, 4, 6, 7, 8, 10)=38
∑(3, 4, 6, 7, 9, 10)=39
∑(3, 4, 6, 8, 9, 10)=40
∑(3, 4, 7, 8, 9, 10)=41
∑(3, 5, 6, 7, 8, 9)=38
∑(3, 5, 6, 7, 8, 10)=39
∑(3, 5, 6, 7, 9, 10)=40
∑(3, 5, 6, 8, 9, 10)=41
∑(3, 5, 7, 8, 9, 10)=42
∑(3, 6, 7, 8, 9, 10)=43
∑(4, 5, 6, 7, 8, 9)=39
∑(4, 5, 6, 7, 8, 10)=40
∑(4, 5, 6, 7, 9, 10)=41
∑(4, 5, 6, 8, 9, 10)=42
∑(4, 5, 7, 8, 9, 10)=43
∑(4, 6, 7, 8, 9, 10)=44
∑(5, 6, 7, 8, 9, 10)=45
∑(1, 2, 3, 4, 5, 6, 7)=28
∑(1, 2, 3, 4, 5, 6, 8)=29
∑(1, 2, 3, 4, 5, 6, 9)=30
∑(1, 2, 3, 4, 5, 6, 10)=31
∑(1, 2, 3, 4, 5, 7, 8)=30
∑(1, 2, 3, 4, 5, 7, 9)=31
∑(1, 2, 3, 4, 5, 7, 10)=32
∑(1, 2, 3, 4, 5, 8, 9)=32
∑(1, 2, 3, 4, 5, 8, 10)=33
∑(1, 2, 3, 4, 5, 9, 10)=34
∑(1, 2, 3, 4, 6, 7, 8)=31
∑(1, 2, 3, 4, 6, 7, 9)=32
∑(1, 2, 3, 4, 6, 7, 10)=33
∑(1, 2, 3, 4, 6, 8, 9)=33
∑(1, 2, 3, 4, 6, 8, 10)=34
∑(1, 2, 3, 4, 6, 9, 10)=35
∑(1, 2, 3, 4, 7, 8, 9)=34
∑(1, 2, 3, 4, 7, 8, 10)=35
∑(1, 2, 3, 4, 7, 9, 10)=36
∑(1, 2, 3, 4, 8, 9, 10)=37
∑(1, 2, 3, 5, 6, 7, 8)=32
∑(1, 2, 3, 5, 6, 7, 9)=33
∑(1, 2, 3, 5, 6, 7, 10)=34
∑(1, 2, 3, 5, 6, 8, 9)=34
∑(1, 2, 3, 5, 6, 8, 10)=35
∑(1, 2, 3, 5, 6, 9, 10)=36
∑(1, 2, 3, 5, 7, 8, 9)=35
∑(1, 2, 3, 5, 7, 8, 10)=36
∑(1, 2, 3, 5, 7, 9, 10)=37
∑(1, 2, 3, 5, 8, 9, 10)=38
∑(1, 2, 3, 6, 7, 8, 9)=36
∑(1, 2, 3, 6, 7, 8, 10)=37
∑(1, 2, 3, 6, 7, 9, 10)=38
∑(1, 2, 3, 6, 8, 9, 10)=39
∑(1, 2, 3, 7, 8, 9, 10)=40
∑(1, 2, 4, 5, 6, 7, 8)=33
∑(1, 2, 4, 5, 6, 7, 9)=34
∑(1, 2, 4, 5, 6, 7, 10)=35
∑(1, 2, 4, 5, 6, 8, 9)=35
∑(1, 2, 4, 5, 6, 8, 10)=36
∑(1, 2, 4, 5, 6, 9, 10)=37
∑(1, 2, 4, 5, 7, 8, 9)=36
∑(1, 2, 4, 5, 7, 8, 10)=37
∑(1, 2, 4, 5, 7, 9, 10)=38
∑(1, 2, 4, 5, 8, 9, 10)=39
∑(1, 2, 4, 6, 7, 8, 9)=37
∑(1, 2, 4, 6, 7, 8, 10)=38
∑(1, 2, 4, 6, 7, 9, 10)=39
∑(1, 2, 4, 6, 8, 9, 10)=40
∑(1, 2, 4, 7, 8, 9, 10)=41
∑(1, 2, 5, 6, 7, 8, 9)=38
∑(1, 2, 5, 6, 7, 8, 10)=39
∑(1, 2, 5, 6, 7, 9, 10)=40
∑(1, 2, 5, 6, 8, 9, 10)=41
∑(1, 2, 5, 7, 8, 9, 10)=42
∑(1, 2, 6, 7, 8, 9, 10)=43
∑(1, 3, 4, 5, 6, 7, 8)=34
∑(1, 3, 4, 5, 6, 7, 9)=35
∑(1, 3, 4, 5, 6, 7, 10)=36
∑(1, 3, 4, 5, 6, 8, 9)=36
∑(1, 3, 4, 5, 6, 8, 10)=37
∑(1, 3, 4, 5, 6, 9, 10)=38
∑(1, 3, 4, 5, 7, 8, 9)=37
∑(1, 3, 4, 5, 7, 8, 10)=38
∑(1, 3, 4, 5, 7, 9, 10)=39
∑(1, 3, 4, 5, 8, 9, 10)=40
∑(1, 3, 4, 6, 7, 8, 9)=38
∑(1, 3, 4, 6, 7, 8, 10)=39
∑(1, 3, 4, 6, 7, 9, 10)=40
∑(1, 3, 4, 6, 8, 9, 10)=41
∑(1, 3, 4, 7, 8, 9, 10)=42
∑(1, 3, 5, 6, 7, 8, 9)=39
∑(1, 3, 5, 6, 7, 8, 10)=40
∑(1, 3, 5, 6, 7, 9, 10)=41
∑(1, 3, 5, 6, 8, 9, 10)=42
∑(1, 3, 5, 7, 8, 9, 10)=43
∑(1, 3, 6, 7, 8, 9, 10)=44
∑(1, 4, 5, 6, 7, 8, 9)=40
∑(1, 4, 5, 6, 7, 8, 10)=41
∑(1, 4, 5, 6, 7, 9, 10)=42
∑(1, 4, 5, 6, 8, 9, 10)=43
∑(1, 4, 5, 7, 8, 9, 10)=44
∑(1, 4, 6, 7, 8, 9, 10)=45
∑(1, 5, 6, 7, 8, 9, 10)=46
∑(2, 3, 4, 5, 6, 7, 8)=35
∑(2, 3, 4, 5, 6, 7, 9)=36
∑(2, 3, 4, 5, 6, 7, 10)=37
∑(2, 3, 4, 5, 6, 8, 9)=37
∑(2, 3, 4, 5, 6, 8, 10)=38
∑(2, 3, 4, 5, 6, 9, 10)=39
∑(2, 3, 4, 5, 7, 8, 9)=38
∑(2, 3, 4, 5, 7, 8, 10)=39
∑(2, 3, 4, 5, 7, 9, 10)=40
∑(2, 3, 4, 5, 8, 9, 10)=41
∑(2, 3, 4, 6, 7, 8, 9)=39
∑(2, 3, 4, 6, 7, 8, 10)=40
∑(2, 3, 4, 6, 7, 9, 10)=41
∑(2, 3, 4, 6, 8, 9, 10)=42
∑(2, 3, 4, 7, 8, 9, 10)=43
∑(2, 3, 5, 6, 7, 8, 9)=40
∑(2, 3, 5, 6, 7, 8, 10)=41
∑(2, 3, 5, 6, 7, 9, 10)=42
∑(2, 3, 5, 6, 8, 9, 10)=43
∑(2, 3, 5, 7, 8, 9, 10)=44
∑(2, 3, 6, 7, 8, 9, 10)=45
∑(2, 4, 5, 6, 7, 8, 9)=41
∑(2, 4, 5, 6, 7, 8, 10)=42
∑(2, 4, 5, 6, 7, 9, 10)=43
∑(2, 4, 5, 6, 8, 9, 10)=44
∑(2, 4, 5, 7, 8, 9, 10)=45
∑(2, 4, 6, 7, 8, 9, 10)=46
∑(2, 5, 6, 7, 8, 9, 10)=47
∑(3, 4, 5, 6, 7, 8, 9)=42
∑(3, 4, 5, 6, 7, 8, 10)=43
∑(3, 4, 5, 6, 7, 9, 10)=44
∑(3, 4, 5, 6, 8, 9, 10)=45
∑(3, 4, 5, 7, 8, 9, 10)=46
∑(3, 4, 6, 7, 8, 9, 10)=47
∑(3, 5, 6, 7, 8, 9, 10)=48
∑(4, 5, 6, 7, 8, 9, 10)=49
∑(1, 2, 3, 4, 5, 6, 7, 8)=36
∑(1, 2, 3, 4, 5, 6, 7, 9)=37
∑(1, 2, 3, 4, 5, 6, 7, 10)=38
∑(1, 2, 3, 4, 5, 6, 8, 9)=38
∑(1, 2, 3, 4, 5, 6, 8, 10)=39
∑(1, 2, 3, 4, 5, 6, 9, 10)=40
∑(1, 2, 3, 4, 5, 7, 8, 9)=39
∑(1, 2, 3, 4, 5, 7, 8, 10)=40
∑(1, 2, 3, 4, 5, 7, 9, 10)=41
∑(1, 2, 3, 4, 5, 8, 9, 10)=42
∑(1, 2, 3, 4, 6, 7, 8, 9)=40
∑(1, 2, 3, 4, 6, 7, 8, 10)=41
∑(1, 2, 3, 4, 6, 7, 9, 10)=42
∑(1, 2, 3, 4, 6, 8, 9, 10)=43
∑(1, 2, 3, 4, 7, 8, 9, 10)=44
∑(1, 2, 3, 5, 6, 7, 8, 9)=41
∑(1, 2, 3, 5, 6, 7, 8, 10)=42
∑(1, 2, 3, 5, 6, 7, 9, 10)=43
∑(1, 2, 3, 5, 6, 8, 9, 10)=44
∑(1, 2, 3, 5, 7, 8, 9, 10)=45
∑(1, 2, 3, 6, 7, 8, 9, 10)=46
∑(1, 2, 4, 5, 6, 7, 8, 9)=42
∑(1, 2, 4, 5, 6, 7, 8, 10)=43
∑(1, 2, 4, 5, 6, 7, 9, 10)=44
∑(1, 2, 4, 5, 6, 8, 9, 10)=45
∑(1, 2, 4, 5, 7, 8, 9, 10)=46
∑(1, 2, 4, 6, 7, 8, 9, 10)=47
∑(1, 2, 5, 6, 7, 8, 9, 10)=48
∑(1, 3, 4, 5, 6, 7, 8, 9)=43
∑(1, 3, 4, 5, 6, 7, 8, 10)=44
∑(1, 3, 4, 5, 6, 7, 9, 10)=45
∑(1, 3, 4, 5, 6, 8, 9, 10)=46
∑(1, 3, 4, 5, 7, 8, 9, 10)=47
∑(1, 3, 4, 6, 7, 8, 9, 10)=48
∑(1, 3, 5, 6, 7, 8, 9, 10)=49
∑(1, 4, 5, 6, 7, 8, 9, 10)=50
∑(2, 3, 4, 5, 6, 7, 8, 9)=44
∑(2, 3, 4, 5, 6, 7, 8, 10)=45
∑(2, 3, 4, 5, 6, 7, 9, 10)=46
∑(2, 3, 4, 5, 6, 8, 9, 10)=47
∑(2, 3, 4, 5, 7, 8, 9, 10)=48
∑(2, 3, 4, 6, 7, 8, 9, 10)=49
∑(2, 3, 5, 6, 7, 8, 9, 10)=50
∑(2, 4, 5, 6, 7, 8, 9, 10)=51
∑(3, 4, 5, 6, 7, 8, 9, 10)=52
∑(1, 2, 3, 4, 5, 6, 7, 8, 9)=45
∑(1, 2, 3, 4, 5, 6, 7, 8, 10)=46
∑(1, 2, 3, 4, 5, 6, 7, 9, 10)=47
∑(1, 2, 3, 4, 5, 6, 8, 9, 10)=48
∑(1, 2, 3, 4, 5, 7, 8, 9, 10)=49
∑(1, 2, 3, 4, 6, 7, 8, 9, 10)=50
∑(1, 2, 3, 5, 6, 7, 8, 9, 10)=51
∑(1, 2, 4, 5, 6, 7, 8, 9, 10)=52
∑(1, 3, 4, 5, 6, 7, 8, 9, 10)=53
∑(2, 3, 4, 5, 6, 7, 8, 9, 10)=54
∑(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)=55

Sono 1024 di cui 208 la cui somma è divisibile per 5
E' corretto?

[Admin]

Si, corretto.

[Quelo]

Io per 1/5 intendo un quinto di tutti i sottoinsiemi

Con insieme {1,..,10} sono 208, circa 1/5 di 1024
Con insieme {1,..,20} sono 209728, circa 1/5 di 1048576
Con insieme {1,..,30} sono 214748416, circa 1/5 di 1073741824

In particolare per insiemi {1,...,5n} vale questa regola $\displaystyle S=\frac{2^{5n}+2^{n+2}}{5}$

Quindi per {1,...,2000} sono $\displaystyle \frac{2^{2000}+2^{402}}{5}$ che è circa 1/5 di $2^{2000}$

[Admin]

Va bene.
Io col "distanti" da 1/5 mi riferivo al fatto che 2^402 nn è qualcosa di così piccolo da essere ignorato .
La soluzione è corretta.
L'hai ricavata per generalizzazione di casi particolari?
Che procedimento hai usato?

[Quelo]

Sono partito testando tutti gli insiemi da 2 a 25 elementi ed il risultato è stato questo:

Codice: Seleziona tutto

(1,...,2), SI=4, S5=1, 5*S5-SI=1
(1,...,3), SI=8, S5=2, 5*S5-SI=2
(1,...,4), SI=16, S5=4, 5*S5-SI=4
(1,...,5), SI=32, S5=8, 5*S5-SI=8
(1,...,6), SI=64, S5=14, 5*S5-SI=6
(1,...,7), SI=128, S5=26, 5*S5-SI=2
(1,...,8), SI=256, S5=52, 5*S5-SI=4
(1,...,9), SI=512, S5=104, 5*S5-SI=8
(1,...,10), SI=1024, S5=208, 5*S5-SI=16
(1,...,11), SI=2048, S5=412, 5*S5-SI=12
(1,...,12), SI=4096, S5=820, 5*S5-SI=4
(1,...,13), SI=8192, S5=1640, 5*S5-SI=8
(1,...,14), SI=16384, S5=3280, 5*S5-SI=16
(1,...,15), SI=32768, S5=6560, 5*S5-SI=32
(1,...,16), SI=65536, S5=13112, 5*S5-SI=24
(1,...,17), SI=131072, S5=26216, 5*S5-SI=8
(1,...,18), SI=262144, S5=52432, 5*S5-SI=16
(1,...,19), SI=524288, S5=104864, 5*S5-SI=32
(1,...,20), SI=1048576, S5=209728, 5*S5-SI=64
(1,...,21), SI=2097152, S5=419440, 5*S5-SI=48
(1,...,22), SI=4194304, S5=838864, 5*S5-SI=16
(1,...,23), SI=8388608, S5=1677728, 5*S5-SI=32
(1,...,24), SI=16777216, S5=3355456, 5*S5-SI=64
(1,...,25), SI=33554432, S5=6710912, 5*S5-SI=128

Si vede subito che il totale dei sottoinsiemi (SI) vale $2^n$ mentre i sottoinsiemi divisibili per 5 (S5) seguono uno schema su base 5:
raddoppio per 3 volte (1>2>4>8) poi raddoppio 2 volte ma togliendo una quota (8>16-2>28-2)
Se facciamo la differenza tra 5 volte S5 e SI lo schema diventa ancora più semplice

Codice: Seleziona tutto

1      2      4      8     16    
2      4      8     16     32	
4      8     16     32     64
8     16     32     64    128
6     12     24     48     96

Da qui si possono ricavare le formule per qualsiasi dimensione dell'insieme di partenza

[Admin]

Sono partito testando tutti gli insiemi da 2 a 25 elementi ed il risultato è stato questo...

Ok, immaginavo.

Condivido la dimostrazione, imparata in questo video youtube, presentato e spiegato davvero molto bene (anche se in inglese):



A me sembra una roba fantascientifica, pur avendola compresa e constatato che funziona anche per altre casistiche (non mi riferisco tanto alle funzioni generatrici, che già sono una roba mindblowing. ma alla parte con i numeri complessi).

Fatemi sapere cosa ne pensate.

P.S.: ne ho approfittato per aggiungere il comando per inserire video youtube in modo embed.


Saluti
Admin

[Gianfranco]

Cari Pietro e Sergio, ho seguito appassionatamente questa discussione e provato anch'io a risolvere il problema. Ho visto il video su Youtube.
Non ho postato nulla perché non avevo nulla di significativo da aggiungere.
Complimenti a voi! Un post interessante, sorprendente e bellissimo!
Grazie!