Question 881130: A number when reversed gets doubled find the number.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! 0 works, and it can provably be shown that 0 is the only nonnegative integer that works.
Let n be the number. Since 2n has the same number of digits as n, the first digit of n must be 1,2,3, or 4. Furthermore, it cannot be 1 or 3, since the reverse of n is even.
Therefore n begins with a 2 or 4, so 2n begins with either 4, 5, 8, or 9. This means that n ends with 4, 5, 8, or 9. However this implies that 2n is congruent to 0, 6, or 8 (mod 10) (by doubling all the units digits), which implies that n begins with 0, 6, or 8, contradiction.
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