Rob Fathauer discusses the ins and outs of the mathematical toy business, and we ask: For which numbers is the sum of digits the same as the sum of digits of twice the number. For example:
The sum of the digits of 351 is 9 and the sum of the digits of 2 x 351 = 702 is also 9.
1) If a number has this property, can we always rearrange its digits and obtain another number with this property (513, 135, etc all have it)
2) Which powers of 2 have this property?
3) And most of all, can you give a simple characterization of the numbers with this property, in terms of just the digits themselves?