Problem 1516. Put m balls into n boxes

Binbin Qi

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Can you find all the cases where, if I put 3 balls into 2 boxes
the case is
   1     1
   1     2
   2     2
   2     2
the columns stand for a ball, the number stands for box, and the row stands for a case.
So we have 4 cases
You should write a function, input m and n, m stand for the number of balls, n stands for the number of boxes, output all the cases.
Example
If m = 3, n = 4 then you should output
   1     1
   1     2
   1     3
   1     4
   2     2
   2     3
   2     4
   3     3
   3     4
   4     4
   2     2
   2     3
   2     4
   3     3
   3     4
   4     4
   3     3
   3     4
   4     4
   4     4

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Last Solution submitted on Aug 25, 2026

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6 Comments

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Andrew Newell on 10 Dec 2014

I don't think you have a complete statement of the problem. Why, in the first example, are arrangements like 1 1 2 excluded? And you only accept the arrangements in a particular order. How do you define the order?

Binbin Qi on 11 Dec 2014

the data ascended by column,when the first column is the same, sort by the second column,...

Andrew Newell on 11 Dec 2014

Thanks - and I realize now that 1 1 2 is not excluded; I just wasn't looking carefully.

Rafael S.T. Vieira on 17 Jul 2020

The best way to generate such a sequence is using depth-first search or recursion. By prohibiting the usage of IFs, all solutions are inefficient (because we can't cut the tree, and are forced to follow all branches).

Doddy Kastanya on 18 Dec 2020

For the 3 balls 2 boxes cases, shouldn't the following be part of the answer as well?
1 2 1
2 1 1
2 1 2
2 2 1

Dyuman Joshi on 6 Oct 2022

Why is 'if' banned, @Binbin Qi? Due to this (stupid, in my opinion) ban, I can not use diff as well. I have put up a temporary change in place, but I suggest you to please fix the problem asap.

And if you are putting up restrictions on the test suite, please mention it in the problem statement.

Also, your own solution and the reference solution do not work.

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