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Marbles in boxes (Posted on 2017-08-16) Difficulty: 4 of 5
How many distinct distributions (x,y,z,w) of n identical marbles in 4 boxes labeled A,B,C and D are there, such that
x,y,z,w are positive integers in strictly increasing order?

Verify the validity of your formula (or set of formulas) by manual listing of all such distributions for n=18.

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts re: solution - OEIS | Comment 4 of 5 |
(In reply to solution by Charlie)

Taking this sequence 1,1,2,3,5,6,9,... and seaching the OEIS yields A001400 "Number of partitions of n into at most 4 parts."  In the comments it is noted that this sequence is the "Number of different distributions of n+10 identical balls in 4 boxes as x,y,z,p where 0<x<y<z<p."
  Posted by Brian Smith on 2017-08-17 11:11:25

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