Find the lowest positive integer that has its digits reversed after dividing it by 2.

If the number begins with a 9, the quotient begins with a 4, so the original number ended in 4.  But with the quotient ending in 9, the original number (twice the quotient) would have to end in 8.  So that's impossible.

Starting with 8, we get 4 also, but the quotient ending in 8 leads to the original number ending with 2. Strike another.

7...3 vs 3...7 is also inconsistent.

6...3 vs 3...6 also.

5...2 vs 2...5 the same.

4...2 vs 2...4 also ng.

3...2 vs 2...3 ditto.

2...1 vs 1...2 the same.

1...0 vs 0...1 likewise, as well as having a leading zero.

So this meaning of the puzzle is out.  Perhaps the mirror is to be taken literally, but that would require calculator-like digits, where 5 is the mirror image of 2, and a restricted set of digits: 1, 2, 5, 8 and 0.

Posted by Charlie on 2004-07-15 09:03:04