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.