Found this problem/puzzle:

100 balls are divided into groups.

The difference between any two groups is at most 2.

In how many ways can this be done?

Permutations are not considered as different.

Example: Using 6 balls, the solution is 9:

(1,1,1,1,1,1), (1,1,1,1,2), (1,1,2,2),

(1,1,1,3), (1,2,3), (2,2,2),

(2,4), (3,3), (6).

I simply don't understand what's being asked.

Like, why is difference between (1,1,1,1,1,1) and (1,2,3) at most 2?

Can anybody explain it?

Thank you.