George Mach posed this problem to one of his classes (out at Cal Poly SLO in California), and my dad passed it along for posting here. The answer may be surprising, in the sense that it’s not something that can be easily guessed. Here’s the question:
Find a whole number ending in 6 which is doubled if you move the 6 from the end to the beginning. (e.g. the number 316 almost works because 631 is close to the double of 316, but not quite)
I’ll post the answer here tomorrow….
There are an infinite number of solutions, the smallest of which is 315,789,473,684,210,526
This problem can also be generalized to ending in a different digit and the permutation being a different multiple; according to Jim Delany (thanks Jim!) the smallest numbers that occur are those that end in 4, 5, 6, 7, 8, 9 and are quadrupled (or quintupled, for the one ending in 7). All of those numbers are less than 300,000.