Number Problem 1

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The sum of a two digit number and the number formed by reversing the digits is a perfect square. Find the numbers.

Solution: If the digit in the ten’s place is x and the unit place is y, then the number is 10x + y.

The number on reversing becomes 10y + x.

Sum of the 2 numbers is

(10x + y) + (10y + x) = 11(x+y)

11(x+y) must be a perfect square.

This is possible only when x+y = 11

The possible number of x and y are given by

(x,y) = (2,9) or (9,2)

(x,y) = (3,8) or (8,3)

(x,y) = (4,7) or (7,4)

(x,y) = (5,6) or (6,5)

Hence, the required numbers are 29,92; 38,83; 47,74; 56,65;

For example, 38 + 83 = 121 = 11²