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Mr. and Mrs. Crazy: Squimes

Math brain teasers require computations to solve.


Puzzle ID:#45263
Fun:** (1.97)
Difficulty:*** (2.9)
Submitted By:CaIceDevilAus****!!




Mr. and Mrs. Crazy were just one step away from winning the $1,000,000 prize in the contest. In order for them to win, they must answer this question:

What are the only ten 8-digit squimes?
In case you don't know what a squime is, it is any number that:
-has no zero
-has all different digits
-starts and ends with a single-digit prime or single-digit square number
-each pair of consecutive digits is a square or prime

Mr. and Mrs. Crazy solved it and won one million dollars. What were their answers?

Open Calculator


A squime cannot contain the number 8 since no square or prime ends with 8.

The largest squime has at most eight digits, since it cannot contain
8 or 0. If we use 2, it must come first because no square or
2-digit prime ends in 2. No 2-digit prime ends in 5 and only 25 is
square. If, therefore, we use 5, it must come after 2. So we begin
with 25.


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Sep 25, 2009

huh? i still didn't get how you got the 25...neways...
(user deleted)
Jan 10, 2010

16432597 works as well. 1, while not considered a prime number, is a square so it fits the rule that the first digit must be either prime or a square.

16 is a square, 43 is prime, 25 is a square and 97 is prime. 7 is of course prime as well.
May 12, 2010

16432597 will not work. The rule about each pair of consecutive digits will cause problems here.

When looking as each pair of digits you have to look at each digit and the one following it. so for 16432597 this would be
16, 64, 43, 32, 35, 97. In this list 32 and 35 are not prime. This is also the reason that 2 has to be the first digit.

I do think there is one additional squime: 25971364

- 1st digit (2) is prime
- digit pairs
25, 59, 71, 13, 36 and 64 are primes or squares
- last digit (4) is a square
Nov 08, 2012

A great problem! I did solve this, though I didnt have the patience to work out all the 11 answers. Thanks a lot!
I have forwarded this to a few people who are interested in math puzzles. They have also appreciated this problem and have requested to me to convey their thanks to you.

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