- #1

- 50

- 0

...........sums: 4 5 6 7 8 9 10 11 12 13 14

combinations: 1 4 10 20 35 56 80 104 125 140 146

...........sums: 15 16 17 18 19 20 21 22 23 24

combinations: 140 125 104 80 56 35 20 10 4 1

I notice that the combination 146 is symmetric about the sum of 14.

I mean each combination for each sum less than 14 is the same as each combination for each sum greater than 14.

Is it possible to find a formula or use Pascal s triangle or anything to find the combination for any sum here WITHOUT listing any outcomes.

How can it be done Thanks.