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June 16th, 2018, 07:26 AM   #1
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Wink Find the number of possible choices for x and y when A=100?

I have some questions during the writing of this post, please read it via https://www.physicslog.com/number-of-choices/
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July 4th, 2018, 11:56 PM   #2
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I agree with your answer = 49 and think your algorithm is OK for any value of A.
Hope you get more replies to this and your other questions with A being the sum of more than two different numbers/
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July 7th, 2018, 04:25 PM   #3
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Yes, there are 49. The positive integer pairs, (x, y), such that x+ y= 100 are (1, 19), (2, 98 ), (3, 97), ... (97, 3), (98, 2), (99, 1).

My first thought was that there were 99 such pairs but then I noticed the conditions that $x\ne y$ and that order is not to be considered. Dropping the pair (50, 50) leave 98 pairs and half of that is 49.
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July 16th, 2018, 01:49 AM   #4
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If you include the pair 0 + 100 = 100, then you have a half pairs for even, and half - 1 pairs for odd.

Last edited by skipjack; July 16th, 2018 at 03:45 AM.
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