Can You Solve The NSA’s Latest Puzzle Problem?

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Casey Harper Contributor
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The National Security Agency posted its “Puzzle Periodical” Tuesday for the month of May, and The Daily Caller News Foundation is willing to make its best guess.

The word puzzle:

Four friends, Holly, Belle, Carol, and Nick, gather for May birthdays. Holly announces that she has a game before dinner. She hid gifts for each of her friends inside three separate boxes secured with padlocks. She challenges her friends to figure out the combination without consulting each other.

She provides the following information. All the padlocks have the same combination. The padlocks use 3 digits from 0 to 9. She also tells them that the sum of the three digits is equal to nine, and every digit is equal to or greater than the previous digit. Holly tells each of her friends one of the digits in the combination. She states, “I’ve given the first digit to Belle, the second digit to Carol, and the third digit to Nick.” The caveat is that the friends cannot share their numbers with each other or they will forfeit the gifts.

Then Holly gives her friends 30 minutes to open the padlocks while she watches and finishes dinner.

The three friends begin to think of the solution. One by one, they each try their hand at their padlock, but none of them opens the padlock. Seeing that no one has succeeded, suddenly Carol realizes she knows the answer, and successfully opens her box, revealing a new fitness tracker. Following this, Nick opens his padlock, revealing a new tablet; and Belle opens her box to find new pair of headphones.

Having watched this entire event unfold, can you determine the correct combination?

Hint: Belle knows her digit is a 1

Here’s TheDCNF’s guess (excluding the potential that any one of them could “brute force” the problem in a limited number of guesses): Belle’s digit is one. Carol’s digit is one. Nick’s digit is seven.

There are several combinations that could work: (1,4,4) (1,2,6) etc. But we chose our combination because of this line: “Seeing that no one has succeeded, suddenly Carol realizes she knows the answer.”

Carol is able to figure out the combination because no one else has yet figured it out. The only way that Carol can figure out the combination because everyone else failed is if she has a one, and she’s waiting to see if Nick immediately knows the answer. If Carol had a four, then any number of failed Nick guesses would not give her the answer.

As a one, Carol knows that Belle has either a one or a zero, which means Nick must have a seven or eight. Here’s the key: Carol knows the answer because, if Nick had an eight, Nick would immediately know the answer because there would only be one possible combination: zero, one, eight. Carol realizes that since Nick doesn’t immediately know the answer, it must mean that Nick has a seven, leaving multiple possibilities for the other digits. Based on the failed guess and her one, Carol instantly knows Nick has a seven, which means Belle must have a one to add to Carol’s one.

Once Carol is able to figure out the answer, Nick realizes that Carol was only able to figure out the problem by knowing that he didn’t have an eight, which means she must have a one, which means Belle must have a one. As the last remaining one, Belle has the same thought process by seeing the other two figured it out.

That’s our best guess, folks. To find out, check back Wednesday for the NSA answer.

Reporters Blake Neff and Geoffrey Ingersoll contributed to this tangle of information that might not end up being right.

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