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?
For each number (1-18) write down its possible partners (e.g. 7 can be paired with 2, 9, or 18). Starting with the numbers that have only one possible partner, make the assignments, and remove both of the numbers from all other possible partner lists. You'll find that there is only one solution, and it is easy to get to.
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