### Brain Teasers

# Mr. and Mrs. Crazy: Squimes

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

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