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June 16th, 2018, 07:26 AM  #1 
Newbie Joined: Jun 2018 From: Nepal Posts: 3 Thanks: 0  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/numberofchoices/ 
July 4th, 2018, 11:56 PM  #2 
Member Joined: Aug 2015 From: Chiddingfold, Surrey Posts: 50 Thanks: 3 Math Focus: Number theory, Applied maths 
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/ 
July 7th, 2018, 04:25 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,244 Thanks: 887 
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. 
July 16th, 2018, 01:49 AM  #4 
Newbie Joined: Aug 2015 From: Montenegro (Podgorica) Posts: 20 Thanks: 2 
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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