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Fill in (Posted on 2004-07-20) Difficulty: 3 of 5
8448 is a multiple of 44. Change the two 4s for different odd numbers X and Y, so 8XY8 can be divided by XY. No computers allowed!

See The Solution Submitted by Federico Kereki    
Rating: 2.7143 (7 votes)

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Solution Puzzle Solution Comment 8 of 8 |
(In reply to answer by K Sengupta)

By the problem, 8XY8 is divisible by XY, so that 8XY8 - 10*(XY) = 8008 is divisible by XY.

Now, 8008 = 7*8*11*13, and accordingly two digit odd numbers that are factors of 8008 are 11, 13, 77, 91.
But, XY = 11, 77 violates the provisions of the problem since X!=Y in that situation.

Consequently,  XY = 13 or 91.

Edited on March 13, 2008, 3:37 pm
  Posted by K Sengupta on 2008-03-13 15:12:57

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