### Brain Teasers

# Mr. and Mrs. Crazy: Squimes

Math
Math brain teasers require computations to solve.

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?

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?

### Hint

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.

### Answer

The 8-digit squimes are:25316479

25316497

25364179

25364197

25364719

25364971

25371649

25971643

25973164

25973641

Hide Hint Show Hint Hide Answer Show Answer

## What Next?

**Solve a Similar Brain Teaser...**

Or, get a random brain teaser.

If you become a registered user you can vote on this brain teaser, keep track of

which ones you have seen, and even make your own.

## Comments

huh? i still didn't get how you got the 25...neways...

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.

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

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

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

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.

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.

## Follow Braingle!