Sunday Times Teaser 2574 – Higher Powers
by Richard England
Published: 21 January 2012 (link)
I have chosen two different two-figure numbers. They use the same two digits as each other, but in different orders. If I start with either number and raise it to a power equal to either of the two numbers, then I find that the answer is a number whose last two digits form the number with which I started.
What are my two numbers?