Cracking Padlocks
In an escape game, you have found a padlock with numbers from 1 to 60. You have previously found a piece of paper inside a clear bottle. On the piece of paper is a picture of a padlock and four clues:
1) Four numbers complete the sequence.
2) No two numbers are the same.
3) The second number is twice the third.
4) The third number is prime.
How many possible combinations exist for the padlock?
The answer is 33060.
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1 solution
There is no trick to this problem, but there is a specific order to think things through. First consider the last clue. There are 10 prime numbers between 1-60 such that its doubled value is also between 1-60 (31 is the 11th prime whose double is 62) .
The second number would be 1 choice, since it is linked with the third number. Because no two numbers are the same, we do the following product: 5 8 × 1 × 1 0 × 5 7 = 3 3 0 6 0 .