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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?

Factoring Factorials

Find the highest power of 11 that will divide into 1000! exactly.

Strange Numbers

Age 11 to 14
Challenge Level

We define "strange" numbers in the following way:

  • All strange numbers are prime.
  • Every single digit prime number is strange. 
  • A number with two or more digits is strange if, and only if, the two numbers obtained from it, by removing either its first or its last digit, are also strange.

Find all strange numbers.

This problem comes from the Hungarian magazine KoMaL. You can find many other challenging problems in English on the KoMaL website.