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Cracking Combinations is a puzzle in Professor Layton and the Azran Legacy. The puzzle must be solved in order to progress the story.
Puzzle
The police have received a warning from a legendary safe-cracker about his next crime:
"Tonight, I plan to break into the bank and take the treasure from one of the safes numbered 1 to 60. I will steal from the one safe whose number cannot be made by adding together any combination of these: 0, 1, 2, 4, 7, 15, 31. (Using each one no more than once per combination, that is.)"
Which safe should the police keep an extra close eye on tonight?
Hints
Solution
Incorrect
Too bad.
Read the legendary safe-cracker's warning one more time, and then give it another go.
Correct
Cracking!
The legendary safe-cracker is targeting safe number 30. The numbers 1-29 and 31-60 can all be made by adding together various combinations of 0, 1, 2, 4, 7. 15, and 31.
30 is the only number between 1 and 60 that cannot be made from these numbers.
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