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'Many Clues, One Answer' printed from http://nrich.maths.org/
Find the number:
it's less than $100$;
it's one more than a multiple of $3$;
exactly one of the digits is prime;
if you reverse its digits, you get a prime;
it has exactly four factors;
the sum of its digits is prime;
if you multiply it by $5$, the answer is greater than $100$.
This problem is taken from the UKMT Mathematical Challenges.