GeekDad Puzzle of the Week Solution: Anagramatic Products

Geek Culture

Last week’s puzzle, as presented:

There are some numbers that, when multiplied by a second number, become anagrams of themselves. For example:

1035 x 3 = 3105
1782 x 4 = 7128

There are fewer numbers that can be multiplied by two or more different numbers and remain anagrams of their former selves. This week’s puzzle: What is the lowest number that remains an anagram of itself when multiplied by 5 different numbers? Note that a number is not considered an anagram of itself and leading zeroes are not allowed.

To qualify for your chance at this week’s $50.00 ThinkGeek gift certificate, please send the number to GeekDad Central. For a second entry into the random drawing, tell me what is special about the number/set of anagrams. Good luck!

The answer to this week’s puzzle is 142857.

2 x 142857 = 285714
3 x 142857 = 428571
4 x 142587 = 571428
5 x 142857 = 714285
6 x 142857 = 857142

The “special” characteristic of this number (142857) is that it is the base of the least known simple repeating decimal. I mean, everyone knows 1/2 is 0.5, 1/3 is 0.3, 1/4 is 0.25, 1/5 is 0.2, and 1/6 is 0.16. But not everyone knows that 1/7 = 0.142857, or 0.142857142857142857… As shown above, each of its multiples are also similarly straightforward to calculate: 3/7 is 0.428571 or 0.428571428571428571… and 6/7 is 0.857142 or 0.857142857142857142…

Thanks to everyone that presented a solution. This week’s winner is John Meck, who not only correct answered the question, but also correctly identified 142857 as relating to the fraction 1/7 and will soon be the proud owner of a $50 ThinkGeek Gift Certificate. Everyone else can use the discount code GEEKDAD93SF to save $10 off a ThinkGeek order of $50 or more.

Liked it? Take a second to support GeekDad and GeekMom on Patreon!