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Puzzle:
"You are to open a safe without knowing the combination. Beginning with the dial set at zero, the dial must be turned counter-clockwise to the first combination number, (then clockwise back to zero), and clockwise to the second combination number, (then counter-clockwise back to zero), and counter-clockwise again to the third and final combination number, whereupon the door shall immediately spring open; there is no handle or key to turn.
The dial has numbers from zero to 40, and the zero is not one of the combination numbers.
Without knowing the combination numbers, what is the maximum number of trials required to open the safe? One trial equals one attempt to dial a full three-number combination, and you must start again from zero for each trial."
- An interesting and carefully worded question.
- What does "the maximum number of trials required to open the safe" mean?
- trials to open the safe + open immediately ---> at last step, we will always try to turn to the maximum number (40) as possible.
- since if the previous two numbers are correct, if we move toward 40 for the last number, the safe will always open.
- Now the question becomes in how many combination the first two numbers can be. (maximum number of trials)
- Thus, the maximum number is 40.
