(For clarity, "A" is the hundred thousands digit, "B" is the ten thousands digit, etc.) X has the following properties: 2X = CDEFAB, 3X = BCDEFA, 4X = EFABCD, 5X = FABCDE, and 6X = DEFABC. What is the value of X?
This proved a lot easier to solve than I thought it would be.
A has to be 1, since anything else would mean that at least two of the numbers would be seven digit numbers. If A=1, then F=7, since that is the only number whose product when multiplied by 3 would end in a 1. Multiplying 7 by 2,4,5 and 6 gives one the remaining numbers: B=4, D=8, E=5, C=2.
The answer is X=142857
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