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 Marbles in boxes (Posted on 2017-08-16)
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 No Rating

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 a kind of solution | Comment 1 of 5
15 distributions were found (admittedly without brain):

1,2,3,12
1,2,4,11
1,2,5,10
1,2,6,9
1,2,7,8
1,3,4,10
1,3,5,9
1,3,6,8
1,4,5,8
1,4,6,7
2,3,4,9
2,3,5,8
2,3,6,7
2,4,5,7
3,4,5,6

Program in the Prolog language:

box(A,B,C,D) :-

between(1,18,A),
between(1,18,B),
between(1,18,C),
between(1,18,D),

A < B,
B < C,
C < D,

N is A+B+C+D,
N is 18.

between(L,U,X) :-
integer(L),integer(U),
(   var(X) ->
L =< U,
between1(L,U,X)
;   integer(X),
L =< X, X =< U
).

between1(L,U,X) :-
(   X = L
;   M is L + 1, M =< U,
between1(M,U,X)
).

Edited on August 16, 2017, 10:31 am
 Posted by ollie on 2017-08-16 10:25:57

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