Math Puzzles Volume 3: Even More Riddles And Brain Teasers In Geometry, Logic, Number Theory, and Probability by Presh Talwalkar

Author:Presh Talwalkar [Talwalkar, Presh]
Language: eng
Format: epub
Published: 2015-07-31T22:00:00+00:00

(where abc means place card a in lock 1, card b in lock 2, and card c in lock 3)

Now, I claim the following: if any of these is the correct combination for the safe, then the safe will open. Why is that? Let's work out a case.

Suppose that abc is the correct combination. When you first try abc, the status of the three locks will change, and the safe may or may not open. But when you do bca and cab, both of these are derangements of abc where none of the cards are in the right spot. Therefore, all three locks will get closed. So when you do abc again, all three locks get opened and the safe will open.

Similarly, this procedure will open the safe if either bca or cab is the correct order for the cards.

If none of these four trials work, then you should do the following procedure, testing if the safe opens after each try.

bac

acb

cba

bac

By similar logic, under this procedure the safe will definitely open if any of bac, acb, or cba is the correct order for the keys.

Through these series of tests, we have created a procedure to test out all 6 possible ways the cards could correspond to their correct locks: abc, bca, cab, bac, acb, or cba. Therefore we have found a way to guarantee we can unlock the safe within 8 tries.

This is good news since it means the safe can get open. The bad side is that it means the safe can easily be cracked by anyone with mathematical sense. Sounds like it's time to get a new safe...

This delightful puzzle was suggested to me by a reader whose website is (written in Italian): Mau.

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