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# Chess tournament Problem

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The contestants in a chess tournament were numbered from 1 to 18. When the players were paired for the first game, the sum of the two numbers for each pair was a perfect square. What were the pairings for the first game?
Jan 27, 2014

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I'm not sure if there is a formula for this type of question but I just went through counting up all the groups. My answers are:
(1,15) (2,14) (3,13) (4,12) (5,11) (6,10) (7,18) (8,17) (9,16)
Jan 28, 2014
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Jedithious:

The contestants in a chess tournament were numbered from 1 to 18. When the players were paired for the first game, the sum of the two numbers for each pair was a perfect square. What were the pairings for the first game?

***
I remember these from one of my logic puzzle books a couple of years ago. It real easy to do.

You have to make a chart like this. 1/2 chart really but I made the whole thing because you can see it easier.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 x---4---------9---------------------------16
2 -x-----------9------------------------16
3 --x------9-----------------------16
4-----x-9----------------------16
5-------x-------------------16
6----------x-----------16
7------------x---16---------------------------------------25
8----------------x-------------------------------------25
9------------------x-------------------------------25
10---------------------x-----------------------25
11-------------------------x---------------25
12-----------------------------x-------25
13----------------------------------x
14---------------------------------------x
15--------------------------------------------x
16-------------------------------------------------x
17-----------------------------------------------------x
18----------------------------------------------------------x

Then where the row and column intersect put in the sum.

Then erace all numbers that are not perfect squares or just put only those in the first place'

Mark off all matchin numbers because a person cant play with himself -- tho when i do I always win the game (haha)

Notice there is only one way to make a 4 so remove all number on row 1 because you can only use them once the numbers removed are 9 and 16
There is only one in each collom any way so you don't have wory about removing them.
Then make a list to keep track like I did at the bottom.
4 is the only one by it self so 1 and 3 have to be used for this.
16 is the only one on the 2s row so we have to use 2 and 14.

keep track list
4(1,3) 16(2,14) 16(4,12) 16(5,11) 25(7,18) 25(8,17) 25(9,16) 25(10,15) 25(12,13)