# Sunday Times Teaser 2684 – How Safe?

*by Robin Nayler*

The combination of a lock with six different digits is formed by concatenating three two-digit primes.

The sum and the product of its six digits are both perfect squares and the combination is a multiple of the difference between this sum and this product.

What is the combination?

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This is easy with a computer but is a bit more interesting on paper.

It is also easy on paper – but not so easy to prove there is no solution if repeated digits are allowed.