TRICKY NUMBERS

Number Theory Level pending

If aabb is a perfect square. Find the value of a+b


The answer is 11.

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2 solutions

Shawn Ong
Aug 5, 2014

Note that a a b b = 11 ( 100 a + b ) aabb = 11* (100a+b) . Then ( 100 a + b ) (100a+b) must be divisible by 11. Since 11 ( 100 a + b ) 11|(100a+b) , the sum of its odd digits minus the sum of its even digits must be divisible by 11. This implies that 11 ( a + b ) 11|(a+b) . Since a , b 9 a,b \le 9 , a + b 18 a+b \le 18 leaving a + b = 11 a+b = 11 as our answer.

Exactly the same way I proceeded. Nice solution

Raushan Sharma - 5 years, 6 months ago
Siddhant Singh
Jun 20, 2014

ONLY ONE FOUR DIGIT NO IN THIS PATTERN IS A PERFECT SQUARE.IT IS 88^2=7744.HERE a+b=7+4=11.

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