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Many Clues, One Answer

Age 11 to 14 Short Challenge Level:

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 $100$.
 
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas. 

 

 

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.