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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.

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Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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Factor Trio

Weekly Problem 45 - 2013
Which of the numbers shown is the product of exactly 3 distinct prime factors?

Little Goldbach

Stage: 3 Short Challenge Level: Challenge Level:1


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.
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