### One of a continuing series

Got this one from the Internet, so no fair going to Google for the answer.

**ABCDEF × 3 = BCDEFA**

Substitute a digit for each letter to provide the correct equation. Post your answer as a comment below. The solution will be provided next week (or sooner).

## Update

No solution given yet. I have not taken the time to solve this, but here are some hints.

Note that A < 4 and A ≠ 0. A ≠ 0 is not stated in the problem, but I’m taking it as assumed. If A > 3, then multiplying by three would produce overflow and a number with more digits.

BCDEFA is divisible by 3, which means ABCDEF is divisible by 3, since both have the same digital root.

BCDEFA is divisible by 9.

That should get people going, so I’m going to give more time to come up with an answer.

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Interesting. Consider the repeating fraction 1/7. It contains 1 and 2, so there are two solutions with A = 1 or 2. But it does not contain a 3, so there is no solution with A = 3.

Pingback: Quiz Question | Skeptical Analysis

$ cat findanswer.py

#!/usr/bin/env python

for num in range(100000, 300000):

answer = int(str(num)[1:] + str(num)[0])

if num * 3 == answer:

print “Found it: %s * 3 = %s” % (num, answer)

$ ./findanswer.py

Found it: 142857 * 3 = 428571

Found it: 285714 * 3 = 857142