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How many ways can I make 42?

Given 7 numbers from 0 up to and including 42. How many different ways can I add them where order does matter and I can use a number more than once?

Also is there a method to it?

Reply 1

mqb2766

Original post by Mathstermind

Given 7 numbers from 0 up to and including 42. How many different ways can I add them where order does matter and I can use a number more than once?

Also is there a method to it?

It would help to see the original question as the wording may be subtle, but I'd probably consider
1 non-zero numbers
2 non-zero numbers
...
7 non-zero numbers (6th triangular number may help here ...)
and multply each by the order factor and sum them up.

There may be a simple relationship which the first few terms would show, try evaluating and reposting?

Edit - assuming I'm interpreting the question correctly, there is probably a more direct way to think about this. The answer is probably the volume of a 6D simplex on 0..42 on each axis.