ABC,CDE × 4 = EDC,CBA

I’m a fan of FiveThirtyEight’s weekly puzzle column The Riddler. This week’s edition is a fairly simple challenge:

If A, B, C, D and E are all unique digits, what values would work with the following equation?
ABC,CDE × 4 = EDC,CBA

This is one of those puzzles that’s fiddly to solve by hand, but dead easy if you write a program. Some quick coding in Small Basic (I’m old-school) reveals that there’s just one solution:

A = 2 B = 1 C = 9 D = 7 E = 8
879,912 = 4 x 219,978

Interestingly, there are no other solutions even if you don’t require every digit to be unique. As well, for this particular equation, a solution only exists when you multiply ABC,CDE by 4 – there are no solutions for any other integer between 2 and 9.

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