Eighteen boys and girls have been assigned numbers 1 -18. Pair the students together
in such a manner that:
• the sum of the numbers of each pair is a square number.
• no students is left out unpaired.
List the nine pair of numbers. What Strategy did you use to solve this problem?
Answers
Given :
Nine pair of boys and girls have been assigned numbers 1 to 18
The sum of each pair is a square.
To Find : the paired numbers
Solution:
9 + 16 = 25
8 + 17 = 25
7 + 18 = 25
6 + 10 = 16
5 + 11 = 16
4 + 12 = 16
3 + 13 = 16
2 + 14 = 16
1 + 15 = 16
These are the above pairs
( 1 , 15) , ( 2 , 14) , (3 , 13) , ( 4 , 12) , ( 5, 11) , ( 6 , 10) . (7 , 18) , ( 8 , 17) , (9 , 16)
No one is left out
Strategy used
Maximum sum can be 18 + 17 = 35
minimum sum can be 1 + 2 = 3
Square numbers in between = 4 , 9 , 16 , 25
Sum of all numbers = 18 * 19/2 = 171
16 , 17 and 18 can be used to make 25 only
Hence sum = 75
left sum = 171 - 75 = 96
and pair left = 9 - 3 = 6
16 * 6 = 96
hence 6 sixteen pairs and 3 pairs of 25 is the only possible combination
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