Posted by **Linda** on Tuesday, November 1, 2011 at 12:22pm.

My science class is pretty small. There are just 18 students in the class. My teacher, Mr. Burnett, has an unusual system for picking lab partners. He has given each student a number from 1 to 18, and on lab days, he pulls two numbers out of a bag to match people up. During our last lab I noticed that the sum of each pairing was a perfect square. How were the partners paired with each other?

- algebra -
**Steve**, Tuesday, November 1, 2011 at 5:13pm
Starting with the biggest,

18+7=25

17+8=25

16+9=25

Now all the numbers 7-10 and 15-18 are taken. That leaves 1,2,3,4,5,6,10,11,12,13,14,15

Taking the easy way out,

1+15=16

2+14=16

3+13=16

4+12=16

5+11=16

6+10=16

There may be other arrangements, but this one falls out the easiest.

- algebra -
**MathMate**, Tuesday, November 1, 2011 at 5:14pm
This is a neat problem!

The hardest ones to match are those from 16 to 18, since we can only match to a total of 25. The rest can match to a total of 16 and the job is done.

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