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Are you able to figure it out? It's a word game that utilizes the latest advancements in computer science.
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Are you able to figure it out? It’s a word game that utilizes the latest advancements in computer science.

The puzzle highlighted a hugely successful outcome in the realm of theoretical computer science, a truly astounding discovery that surprised even those well-versed in the subject.

We will revisit the PCP theorem at a later time. But for now, let’s focus on the challenge!

This is a word game where clues in the style of crossword puzzles refer to a column in a vertical layout. The solution for each clue is a three-letter word formed from the three letters indicated by the clue.

Each clue points to the three letters in the answer.

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Would you like to work on this one with me? What is an animal with three letters? How about “bat”?

proj-games 5

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Whenever we provide a compelling response, we receive one point for each letter. “Bat” would give us a total of three points.

Next, let’s continue. Here is one method for filling in the grid.

The red letters are ones not included in the solution.

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Please note that this grid is not a complete solution. The three top clues have been fully answered. I have highlighted the green arrows from the clue ‘verb’, which indicates ‘pay’. However, the three bottom clues have only been partially solved. While ‘food’ matches with ‘pey’, not ‘pea’. We can still give ourselves a point for any letters that are potentially correct in the answer, so ‘pey’ earns us 2 points for the two correct letters in ‘pea’. The total score is 15 points.

Here is a way to obtain a complete solution, resulting in a maximum score of 18. Of course, using “cat” as a starting point would have been much more clear.

puzz 1View image in fullscreen

According to Dana Moshkovitz, a computer science professor at the University of Texas at Austin, the purpose of this puzzle is to embrace a partial solution, as this adds to the enjoyment. The goal is to achieve the maximum score.

Here are three instances, listed from least to most challenging.

Problem 1

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Problem 2

In this puzzle, the clues are more ambiguous: Some clues are synonyms for the answer, and some are descriptions of the answer. Thus ‘exclamation’ refers to an exclamation.View image in fullscreen

Problem 3

Now the clues are even more ambiguous.View image in fullscreen

I will return at 5pm UK time with multiple complete solutions. In the meantime, please refrain from giving away any plot details. Let’s instead talk about our top three letter words.

UPDATE: The solutions are now available for viewing here.

If there are any creative readers who would like to create an interactive version of this puzzle, please include the link below.

What is the relevance of these puzzles to one of the key findings in computer science? Please be patient.

Half a century ago, researchers in computer science realized that numerous problems found in nature, like determining the most efficient way to stack a variety of suitcase sizes in the trunk of a car, become extremely intricate when scaled up and cannot be solved by computers in a practical amount of time. Surprisingly, it has been discovered that finding approximate solutions to these suitcase-in-a-boot problems is equally challenging.

The comparison to the current puzzle is that while it does have a correct answer, it also has “close” answers. As we’ve observed, you can achieve a full score, or a partial score. Consider if this type of puzzle were to have more hints, letters, and arrows. The differentiation between puzzles with a flawless solution and those with a partial solution is so intricate that computers cannot analyze it in a reasonable timeframe.

This subject, known as the “hardness of approximation,” is closely related to the PCP theorem, an impressive discovery related to mathematical proofs. Typically, examining a mathematical proof involves verifying each line to ensure its accuracy, similar to how a teacher checks a student’s work to confirm the logical progression.

The PCP theorem demonstrates that it is not necessary to meticulously review a proof line by line to ensure accuracy. Instead, the proof can be reformulated in a manner where only a small number of randomly selected bits need to be checked, typically two or three bits at two or three points throughout the proof. Remarkably, this method applies to all types of mathematical proofs.

Dana Moshkovitz explains that the above puzzle is a modified version of the PCP theorem, which she created to teach her students about the topic. She further states that almost all current findings on the difficulty of approximation rely on the PCP theorem in its puzzle form.

This can be somewhat confusing because the puzzle itself is not focused on verifying proofs. However, you can view each word as a form of confirmation for a complete solution.

The Probabilistically Checkable Proof (PCP) theorem was a significant breakthrough in theory, with potential for practical applications. It allows a computer with limited memory to efficiently verify if a larger computer has accurately completed a task, such as an iPhone checking the reliability of a cloud program. This technology is currently being utilized in blockchains, including by tech company StarkWare from Israel.

If you want to learn more about the PCP theorem, here’s a great piece by Dana that was in XRDS, the student magazine of the Association for Computing Machinery.

Currently, I am the resident science communicator at the Simons Institute for the Theory of Computing at the University of California, Berkeley.

Since 2015, I have been presenting a puzzle every other Monday. I am constantly searching for intriguing puzzles and welcome suggestions via email.

Source: theguardian.com