Both a and b are four-digit numbers and one is obtained from the other by reversing the digits.

Determine them, knowing that 2 * (a + b) = 5 * (b - 1).

Show your reasoning.

Let a = 1000w + 100x + 10y + z

2002 (w+z) + 220(x+y) = 5000w + 500x + 50y +5z - 5

Now, left hand side is even hence right hand side even.  This imples that z is odd.  Also, right hand side divisible by 5 implies that (w+z) = 5 OR 10 OR 15.  Used brute force with smaller possibilities and got 6359

Posted by Andre on 2005-09-16 19:13:05