algebra

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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 -

    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 -

    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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