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A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

Thirty Six Exactly

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

Strange Numbers

All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either its first or its last digit. Find all strange numbers.

Little Goldbach

Age 11 to 14 Short
Challenge Level

Answer: 5

The numbers are 1, 2, 3, 11 and 17. Note that, because 2 is the only even prime, the only way we can sum two primes to give an odd number is to sum the odd number before it (if it is a prime) and 2.

One of the oldest unsolved problems in number theory is Goldbach's conjecture, which says that every even number (except 2) can be written as the sum of two primes. Perhaps you could be the first to prove it...
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.