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Last active February 18, 2017 01:15
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Find the magic number
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magic_number.md

Find the magic number

The goal is to find the smallest number (let's call it M) such that:

  • If M obeys property X, then the digit X is part of the number.
  • If M does not obey property X, then the digit X is NOT part of the number.

For example, if 2457 were a magic number, it would obey properties 2, 4, 5, 7 and not 0, 1, 3, 6, 8, 9. However we find that not to be the case, so it is not the number we are looking for.

Properties

  • 0. One of the digits of M is the sum of the others.
  • 1. Digits in decreasing sequence.
  • 2. M has at least 2 odd digits.
  • 3. All digits are different.
  • 4. There is no subset in the digits with a sum of 4.
  • 5. The number is not a palindrome.
  • 6. The number does not contain 3 odd digits in a row.
  • 7. M is a prime number.
  • 8. M has at least 2 even digits in a row.
  • 9. The product of all odd digits is a square number.
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