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Topic: Sum of possible combination (Read 470 times) |
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Viperdude619
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Suppose x and y are whole numbers, with x < y. Find the sum of all the sums of all the numbers in unique combinations of whole numbers between x and y, inclusive.
I know that's a mouthful, so I'll give an example below.
Say x = 1 and y = 3. We then are looking at the numbers 1 through 3, or {1, 2, 3}, to work with. We want to find all the possible unique combinations of these numbers. They would be:
{1},
{2},
{3},
{1, 2},
{1, 3},
{2, 3},
{1, 2, 3}.
That's all of them. So we want the sum of all of the sums of the numbers in each combination, so we'd have
(1) + (2) + (3) + (1 + 2) + (1 + 3) + (2 + 3) + (1 + 2 + 3) = 24.
Get it? I hope so. So what I'm asking you is to give me a general formula to find this number, given any x and y.
If I didn't explain this well enough, please let me know, and I'll try to do a better job. I know it's strangely wordy.
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SWF
Uberpuzzler
Posts: 879
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Re: Sum of possible combination
« Reply #1 on: Feb 14th, 2004, 7:42pm » |
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This one probably belongs in the Easy or Medium section. Hard problems should take more than a minute to solve (solution hidden, highlight to read):
(y*(y+1)-x*(x-1))*2y-x-1.
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