problem number 06, Let me count the ways.txt

problem number: 06, Let me count the ways
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QUESTION:-
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It can be useful to know how to break down a number - usually this is done with factors, but instead, let's try it with summable components. For a number, you can work out the possible combinations of non-negative integers which sum to that number. For example, these are the combinations of three numbers which sum to 3:
0 0 3
0 1 2
0 2 1
0 3 0
1 0 2
1 1 1
1 2 0
2 0 1
2 1 0
3 0 0


The digit "1" occurs 9 times above. For your input, how many times does the character "1" appear in all combinations summing to that number?

Note the number "11" would be twice, "21" once, so 1 21 11 would be 4 times.

GIVEN INPUT:-
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3 numbers which sum to 123

ANSWER:-
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q)fun:{a:3?(0 + til 124); b:((sum a) = 123);if[b=1i;list,:enlist a]}
q)
q)
q)i:0
q)
q)
q)while[i<20000000;fun[];i+:1]
q)
q)sum (sum each (raze each string(distinct list)) = "1")
6927i