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The New York Times

The learning network | fun and games: solving math puzzles.

Fun and Games: Solving Math Puzzles

Academic Skills

Teaching ideas based on New York Times content.

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Overview | Why do people like to solve puzzles? How are they good learning tools? In this lesson, students try to solve math puzzles and explain the strategies used to come to the solutions. Students will hone their problem solving skills and their ability to explain their process. They will come away with a broader view of “math” and see its recreational capacity.

Materials | Toothpicks, 9 for each student or pair; materials for puzzle stations, including paper copies of puzzles, blank paper and computer stations if available

Warm-Up | Give each student or pair of students 9 toothpicks, and challenge them to complete the following two tasks, working alone or with a partner:

• Arrange the toothpicks to spell out the number 100.
• Change “100” to the word “cat” by moving only two toothpicks.

Allot enough time for trial and error, and when a solution is found, have students discuss how they found the answer. Pair students who had success with students who struggled and have them work together to go through the puzzle again. (For answers to these tasks, see this TierneyLab post , including the reader comments.)

Next, invite students to share aloud what games or puzzles they use for recreation. Remind them that many puzzles and strategy games are hidden in common places, like online and video games. List the games and puzzles on the board. Have them look at the list and think about what kinds of strategies and types of thinking they use to do these games and puzzles; list these on the board as well.

Ask: Does it surprise you at all to think about the games and puzzles that you do for fun as good ways to engage in strategic and mathematical thinking? If so, why? How is doing puzzles different from doing textbook math problems? If you enjoy solving a puzzle, does that facilitate the learning process? If so, how and why? If not, why not?

Related | In the article “For Decades, Puzzling People With Mathematics,” John Tierney, who writes the New York Times blog TierneyLab , explores the life and work of Martin Gardner, who, at 95 years of age and still writing on his typewriter, has completed over 70 books of “recreational math” puzzles to date:

It never occurred to me that math could be fun until the day in grade school that my father gave me a book of 19th-century puzzles assembled by Mr. Gardner — the same puzzles, as it happened, that Mr. Gardner’s father had used to hook him during his school days. The algebra and geometry were sugar-coated with elaborate stories and wonderful illustrations of giraffe races, pool-hall squabbles, burglaries and scheming carnival barkers. (Go to nytimes.com/tierneylab for some examples.) […] “If all sentient beings in the universe disappeared,” he writes, “there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime even if no one had proved them prime.” I share his mathematical Platonism, and I think that is ultimately the explanation for the appeal of the puzzles. They may superficially involve row boats or pool halls or giraffes, but they’re really about transcendent numbers and theorems. When you figure out the answer, you know you’ve found something that is indisputably true anywhere, anytime. For a brief moment, the universe makes perfect sense.

Read the entire blog post with your students, using the questions below.

Questions | For discussion and reading comprehension:

• How did Gardner fall into the career of becoming a successful puzzle maker?
• Gardner borrowed his puzzles from other sources, including that of a puzzle written for Emperor Charlemagne, 12 centuries ago. In your opinion, why do you think puzzles last over large spans of time?
• In the article, Mr. Gardner states, “The big secret of my success as a columnist was that I didn’t know much about math.” Explain what Gardner means by this statement.
• How does Gardner relate puzzle-solving to the theory of evolution?

RELATED RESOURCES

From the learning network.

• Student Crossword Archive
• Lesson: Doing the KenKen
• Lesson: The Rules of the Game

From NYTimes.com

• Times Topics: Puzzles

Around the Web

• Gathering for Gardner
• MathPuzzle.com
• Interactive Mathematics Miscellany and Puzzles

Activity | Set up various puzzle stations in your classroom, using the following resources, as available and as desired:

• The puzzles on the handout Fun and Games: Classic Puzzles (PDF) (all of the puzzles are on one sheet and can be copied and snipped apart for separate stations; the answers are provided on the second page)
• The weekly puzzles on TierneyLab
• The Times’ online KenKen , Sudoku or Set puzzles
• The interactive feature “The Monty Hall Problem”
• Math puzzle Web sites, like those provided in the Additional Resources box above

Have students move through as many stations as they can during the class period, working individually or in pairs. While they complete each puzzle, they should keep a written log with the puzzle name and the steps they took to solve it, as well as any strategies they would suggest using if they were teaching the solution to others.

At the end of class, reconvene the class for a debriefing discussion. Ask: Which puzzles were the hardest? Easiest? Which were the most fun? Why? What strategies did you use to solve them? How might you help a friend who was stuck on one of these puzzles? What advice or suggestions would you give for tackling the puzzle?

Conclude by discussing both the learning and recreational value of puzzles. Ask: Do you like to solve puzzles? Why or why not? Do you think solving puzzles is an effective way to learn some mathematical skills? If so, which ones, and why? If not, why not?

Going Further | Individually, students write a puzzle of their own, and include a statement (in a paragraph or two) explaining the idea behind their puzzle, the math skills it is designed to teach or test, the types of strategies and thinking involved, and why it should be fun and engaging to do the puzzle.

In a future class, have students bring in their puzzles and test them in class. Compile the puzzles into a booklet that could be shared within the school and community, or perhaps with future classes.

Teachers: How do you use puzzles — whether math or any other kind — for learning?

Standards | From McREL, for Grades 6-12:

Mathematics 1- Uses a variety of strategies in the problem-solving process. 9- Understand the general nature and uses of mathematics.

Thinking and Reasoning 2 – Understands and applies basic principles of logic and reasoning. 5 – Applies basic trouble-shooting and problem-solving techniques.

Writing 1 – Uses the general skills and strategies of the writing process.

Working With Others 4 – Displays effective interpersonal communication skills.

Comments are no longer being accepted.

Randy, More on math puzzles. Dad

off the topic, i have been looking for a good explanation of why a negative times a negative equals a positive. neg 5 dollars in my checking account times negative 10 dollars in your checking account certainly does not equal positive 50 dollars for us to split. I dont understand how nothing x nothing equals something?? can anyone help me with this?

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5 Tips for Solving The New York Times Crossword Puzzle

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To the uninitiated, crossword puzzles are opaque, enigmatic black holes into which intellectual self-esteem is swallowed. Ah, but it doesn't have to be this way! With a bit of strategy and effort, anyone can solve a crossword puzzle — even the legendary crossword from The New York Times.

Turns out, crossword puzzles aren't akin to IQ tests. Nor are they reliant on a massive vocabulary arsenal. The key is to understand the universe in which the puzzle — and its clues — operates.

Let's start with some advice from the Gray Lady herself. If you're a beginning puzzler, start with the Monday crossword and stick with Mondays until you gain some mastery. Why? Each day of the week, from Monday onward, The New York Times' crossword puzzle becomes more difficult, culminating in the most challenging of all: Saturday's crossword. Think Sunday's crossword is even more challenging? Not so. The Sunday puzzle typically has a midweek difficulty rank.

Here are five tips from some experts that will certainly help you to hone your crossword solving skills. So sharpen your pencil or, if you're really brave, pull out your pen, and let's get to solving:

• Know the Lingo
• Preserve the Tense
• Start With the Easy Ones
• Leverage Your Answers
• Use Outside Resources

1. Know the Lingo

For starters, you'll want to familiarize yourself with a few crossword basics. For example, if an abbreviation is called for, you'll see "abbr." If you see the word "letters" as a clue, it refers to an abbreviation. For example, if "hospital ward's letters" is the clue, then "ICU" could very well be the answer.

Here are a few more examples of hidden messages in crossword clues that will help direct you to the proper answer:

Question mark : A question mark at the end of a clue means that it shouldn't be taken at face value. The answer is likely to be a red herring or misdirection — probably a pun, or some other type of wordplay.

Pairings : Pairings often use the word "partner." For example, if the clue is "cause partner," then "effect" may be the answer — because people often pair together the words "cause and effect."

Perhaps or maybe : The clue is meant to be an example of the answer. For example, a clue that reads "sign direction, perhaps" may be "stop" because sometimes signs are stop signs; "keep cold, maybe" might be "refrigerate."

Slang : The answer will often be a slang word if you see the word "familiarly" in the clue. For example, if the clue is "enjoyed, familiarly" a three-letter answer would be "dug."

2. Preserve the Tense

Pay attention to the tense in which the clue is given. A clue of "trade cross words" would have an answer that also is in the present tense, which means that "bicker" or "argue" would be potential answers, depending on the number of spaces available.

To complicate matters, this advice doesn't always hold true. The answer could be in another grammatical tense. If the clue is "nurse," the answer could simply be the noun form of this word: "caregiver." Or, it could be a verb that may not seem as closely associated, such as "breastfeeding" or, as in the case of crying into one's beer, "nursing."

If you encounter a homonym , this signals that the answer will be spelled or pronounced like the clue, but will vary in its meaning. The word, "lead" may refer to metal or an action verb, like "lead" the horse.

3. Start With the Easy Ones

If all this seems rather confusing, take heart. Becoming a solver simply means thinking your way into the puzzle, and you will get better at this over time. Focus first on the short answers and the ones with easily understandable clues. Don't worry about finishing an entire puzzle until you have the short answers down and can replicate your success several times. Why? These short answers are often replicated from puzzle to puzzle and eventually you will learn to recognize them.

When you begin a new puzzle, scan the clues for answers that seem obvious. Pencil (or type) those in, paying close attention to fill-in-the-blank clues, abbreviations and the like.

"I always speed through it on first pass," says Nate Runkel, editor-in-chief of Yo That's My Jawn and an avid puzzler. "Don't get hung up on a clue. Read it, and if you don't know it right away, skip to the next one. Let the second pass be the one where you read and think. That first pass will fill in some letters on the opposite directions that will assist in better identifying the right word on the second."

4. Leverage Your Answers

Once you have a good start on the crossword, confirm your answers by trying to solve the clue that intersects with them. If you answered "cat" to the clue "black Halloween animal," but find that the crossing word doesn't fit with this answer, rethink your options. The answer could be "bat" instead.

Conversely, you can use this "crossing" method to help solve clues that have you stumped.

"Even if you can't fill in the word entirely, fill in what you can," says Brian Donovan, CEO of Timeshatter . "For example, if you know that the answer has to either be 'hats' or 'caps,' fill in the "_a_s" since you are certain about those two letters. This might help you solve the surrounding words more easily."

5. Use Outside Resources

Even The New York Times recommends looking up answers to clues you can't solve. Crosswords are, after all, a game. And games are meant to be both engaging and entertaining — not maddening. There are several online guides that offer answers.

Collaboration is another option. While you may have a depth of knowledge in a certain area, such as medicine, a friend may be a classical music afficionado. Pairing up could be of great benefit to you both.

"If you get stuck, you can ask friends to help you solve it," says James Green, owner, Build A Head , who also recommends tenacity. "The more you do crosswords, the better your mind will be at solving them."

There have only been four editors of The New York Times crossword puzzle, beginning with Margaret Farrar, who was editor of the first puzzle until 1969. Will Weng and Eugene Maleska followed in her footsteps, and Will Shortz took over in 1993.

Please copy/paste the following text to properly cite this HowStuffWorks.com article:

A Quick Puzzle to Test Your Problem Solving (via NYT)

This fantastic test was posted by the New York Times over a year ago:

Here’s how it works:

We’ve chosen a rule that some sequences of three numbers obey — and some do not. Your job is to guess what the rule is. We’ll start by telling you that the sequence 2, 4, 8 obeys the rule:

Now it’s your turn. Enter a number sequence in the boxes below, and we’ll tell you whether it satisfies the rule or not. You can test as many sequences as you want.

[ click here to go to the NYT link and test your answer ]

*SPOILER BELOW*

The answer was extremely basic. The rule was simply: Each number must be larger than the one before it. 5, 10, 20 satisfies the rule, as does 1, 2, 3 and -17, 14.6, 845. Children in kindergarten can understand this rule. But most people start off with the incorrect assumption that if we’re asking them to solve a problem, it must be a somewhat tricky problem. They come up with a theory for what the answer is, like: Each number is double the previous number. And then they make a classic psychological mistake. They don’t want to hear the answer “no.” In fact, it may not occur to them to ask a question that may yield a no. Remarkably, 77 percent of people who have played this game so far have guessed the answer without first hearing a single no. A mere 9 percent heard at least three nos — even though there is no penalty or cost for being told no, save the small disappointment that every human being feels when hearing “no.” It’s a lot more pleasant to hear “yes.” That, in a nutshell, is why so many people struggle with this problem. Confirmation Bias This disappointment is a version of what psychologists and economists call confirmation bias. Not only are people more likely to believe information that fits their pre-existing beliefs, but they’re also more likely to go looking for such information. This experiment is a version of one that the English psychologist Peter Cathcart Wason used in a seminal 1960 paper on confirmation bias. (He used the even simpler 2, 4 and 6, rather than our 2, 4 and 8.) Most of us can quickly come up with other forms of confirmation bias — and yet the examples we prefer tend to be, themselves, examples of confirmation bias. If you’re politically liberal, maybe you’re thinking of the way that many conservatives ignore strong evidence of global warming and its consequences and instead glom onto weaker contrary evidence. Liberals are less likely to recall the many incorrect predictions over the decades, often strident and often from the left, that population growth would create widespread food shortages. It hasn’t. This puzzle exposes a particular kind of confirmation bias that bedevils companies, governments and people every day: the internal yes-man (and yes-woman) tendency. We’re much more likely to think about positive situations than negative ones, about why something might go right than wrong and about questions to which the answer is yes, not no. Sometimes, the reluctance to think negatively has nothing to do with political views or with a conscious fear of being told no. Often, people never even think about asking questions that would produce a negative answer when trying to solve a problem — like this one. They instead restrict the universe of possible questions to those that might potentially yield a “yes.” Government Policy In this exercise, the overwhelming majority of readers gravitated toward confirming their theory rather than trying to disprove it. A version of this same problem compromised the Obama administration’s and Federal Reserve’s (mostly successful) response to the financial crisis. They were too eager to find “green shoots” of economic recovery that would suggest that the answer to the big question in their minds was, just as they hoped and believed: “Yes, the crisis response is aggressive enough, and it’s working.” More damaging was the approach that President George W. Bush’s administration, and others, took toward trying to determine whether Iraq had weapons of mass destruction a decade ago — and how the Iraqi people would react to an invasion. Vice President Dick Cheney predicted in 2003, “We will, in fact, be greeted as liberators.” Corporate America Corporate America is full of more examples. Executives of Detroit’s Big Three didn’t spend enough time brainstorming in the 1970s and 1980s about how their theory of the car market might be wrong. Wall Street and the Fed made the same mistake during the dot-com and housing bubbles. To pick an example close to home, newspapers didn’t spend enough time challenging the assumption that classified advertisements would remain plentiful for decades. One of the best-selling business books in history — about negotiation strategy — is “Getting to Yes.” But the more important advice for us may instead be to go out of our way to get to no. When you want to test a theory, don’t just look for examples that prove it. When you’re considering a plan, think in detail about how it might go wrong. Some businesses have made this approach a formal part of their decision-making: Imagine our strategy has failed; what are the most likely reasons it did? As Jason Zweig has written in The Wall Street Journal, “Gary Klein, a psychologist at Applied Research Associates, of Albuquerque, N.M., recommends imagining that you have looked into a crystal ball and have seen that your investment has gone bust.” When you seek to disprove your idea, you sometimes end up proving it — and other times you can save yourself from making a big mistake. But you need to start by being willing to hear no. And even if you think that you are right, you need to make sure you’re asking questions that might actually produce an answer of no. If you still need to work on this trait, don’t worry: You’re only human.

For unlimited free puzzles, visit www.kenkenpuzzle.com

"The most addictive puzzle since Sudoku"

Will Shortz, New York Times Crossword Puzzle Editor.

Rules For Playing KenKen®

The numbers you use in a KenKen puzzle depends on the size of the puzzle grid you choose. A 4 x 4 grid (4 squares across, 4 squares down) means you use the numbers 1, 2, 3 and 4. In a 6 x 6 grid, use the numbers 1 to 6. An 8x8 grid requires you use the numbers 1 to 8, and so on.

The numbers in each heavily outlined set of squares, called cages, must combine (in any order) to produce the target number located in the top corner of that cage using the mathematic operation indicated (+, -, ×, ÷).

The goal is to fill in all the squares so that each number is used in each row and column and no numbers are repeated in any row or column.

Here's how you play:

• Do not repeat a number in any row or column.
• Cages with just one square should be filled in with the target number in the top corner.
• A number can be repeated within a cage as long as it is not in the same row or column.

Unlimited KenKen puzzles...all sizes...all difficulty levels

Will Shortz Teaches KenKen

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New York Times Crossword Archive

Learn how to access the New York Times Crossword Archive and play archived Crossword puzzles. 

Visit The New York Times Crossword Archive to view past puzzles that can be downloaded and played offline. The New York Times Crossword archive goes back over ten years meaning players can keep solving even after the daily crossword is done!  

Select an option below to learn more:

Where to Play Archived Puzzles

Games and All Access subscribers have access to the Archive. If you do not have a Games or All Access subscription, you have limited access to the Archive.  

To access the Crossword Archives in the Games App, select the Archives tab from the bottom of the app home screen. 

In the Archive you can toggle between The Crossword and The Mini archive using the tabs at the top. Change the date at the top of the calendar screen to navigate through each archive by month and year:

Web Browser

When playing on the web you can access archived puzzles from the Games homepage:

• Select Crossword Archives from the drop-down menu:

In the Crossword Archives you can toggle between the Daily and Mini archive using the tabs at the top. Change the date at the top of the calendar screen to navigate through each archive by month and year:

How to Play a Puzzle From the Archive

• Navigate to the Archive tab at the bottom of the Games app homepage. 
• Select either The Crossword or The Mini .
• Select the month and year you would like to see puzzles from.
• Select the puzzle you would like to play. This will download the puzzle. If the puzzle has already been downloaded to your device, no arrow will appear on the puzzle in the calendar view and it will open upon selection. 
• Select the puzzle again to begin play. 

Note : Y ou may need to restore your network connection to sync puzzle progress with other devices and on the web. 

• From the Crossword Archive select either Daily or Mini .
• Choose a month and year to show puzzles from that timeframe.
• Select the puzzle you would like to play.

Removing Downloaded Puzzles From Your Device

You can remove a downloaded puzzle on the Games app from your device in the Archives tab by pressing down on the puzzle icon. 

A pop-up window will appear, allowing you to “ delete puzzle ”. Your progress will not be lost if you remove a downloaded puzzle from your device. To view your progress, redownload the puzzle. 

Note : By deleting a puzzle, you are simply removing the downloaded puzzle from your device. You can always re-download the puzzle if you wish. 

• On Android devices, downloaded puzzles are automatically removed when you log out of the app. 
• On iOS devices, downloaded puzzles are automatically removed from your device if they were solved more than 30 days prior. 

Archive Icons Glossary

This section provides meanings for each of the puzzle icons in the Archive :

This puzzle is unavailable right now. 

A new puzzle is available.

This puzzle is not available offline.

This puzzle is downloaded, but not solved.

This puzzle is correctly solved.

This puzzle was correctly solved and qualified for a streak. 

This puzzle was correctly solved and qualified for a streak, but has not been downloaded to a device.

These puzzles represent a streak (which can be as few as 2 days). 

This puzzle was incorrectly completed and therefore not solved.

The amount of blue squares filled in each of the above puzzle images indicates your puzzle progress (from start to finish). 

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NYT Connections: hints and answers for Saturday, July 6

Connections  is the latest puzzle game from the New York Times. The game tasks you with categorizing a pool of 16 words into four secret (for now) groups by figuring out how the words relate to each other. The puzzle resets every night at midnight and each new puzzle has a varying degree of difficulty. Just like Wordle , you can keep track of your winning streak and compare your scores with friends.

How to play Connections

• Hints for today’s Connections
• Today’s Connections answers

Some days are trickier than others. If you’re having a little trouble solving today’s Connections puzzle, check out our tips and hints below. And if you still can’t get it, we’ll tell you today’s answers at the very end.

In Connections , you’ll be shown a grid containing 16 words — your objective is to organize these words into four sets of four by identifying the connections that link them. These sets could encompass concepts like titles of video game franchises, book series sequels, shades of red, names of chain restaurants, etc.

There are generally words that seem like they could fit multiple themes, but there’s only one 100% correct answer. You’re able to shuffle the grid of words and rearrange them to help better see the potential connections.

Each group is color-coded. The yellow group is the easiest to figure out, followed by the green, blue, and purple groups.

Pick four words and hit  Submit . If you’re correct, the four words will be removed from the grid and the theme connecting them will be revealed. Guess incorrectly and it’ll count as a mistake. You only have four mistakes available until the game ends.

Hints for today’s Connections

We can help you solve today’s Connection by telling you the four themes. If you need more assistance, we’ll also give you one word from each group below.

Today’s themes

• BIOLOGICAL BUILDING BLOCKS
• PURCHASE FOR A BABY
• OBJECTS PLAYED AS INSTRUMENTS

One-answer reveals

• BIOLOGICAL BUILDING BLOCKS – ATOM
• PURCHASE FOR A BABY – BOTTLE
• OBJECTS PLAYED AS INSTRUMENTS – JUG
• _____ TAG – DOG

Today’s Connections answers

Still no luck? That’s OK. This puzzle is designed to be difficult.  If you just want to see today’s Connections answer, we’ve got you covered below:

• BIOLOGICAL BUILDING BLOCKS – ATOM, CELL, MOLECULE, PROTEIN
• PURCHASE FOR A BABY – BOTTLE, CRIB, MOBILE, RATTLE
• OBJECTS PLAYED AS INSTRUMENTS – JUG, SAW, SPOONS, WASHBOARD
• _____ TAG – DOG, FREEZE, PHONE, PRICE

Connections  grids vary widely and change every day. If you couldn’t solve today’s puzzle, be sure to check back in tomorrow.

Editors’ Recommendations

• Wordle Today: Wordle answer and hints for July 6
• NYT Mini Crossword today: puzzle answers for Friday, July 5
• NYT Connections tips: how to win Connections every day
• If you love Wordle and Connections, Puzzmo may be your next daily obsession
• Move over, Wordle: The New York Times has a new puzzle game

If you logged onto Twitter exactly one year ago, you can probably recall the moment you began to see your feed fill up with gray, yellow, and green boxes. Though it launched in 2021 and gained mainstream popularity in December of that year, Wordle became a sudden cultural phenomenon in early 2022 that was inescapable outside of a muted words list. It was a rare gaming success story, one that could reach a broad audience thanks to its elegant simplicity.

Wordle’s fortune would escalate just as quickly as its user base. In late January 2022, the New York Times announced it had acquired the puzzle game from creator Josh Wardle in an undisclosed, low-seven-figure deal -- a left-field move that almost eclipsed Sony’s announcement that it was acquiring Destiny 2 developer Bungie just hours earlier. The move would spark some worry among fans, who feared that a corporate takeover of the most independent game imaginable could steal its soul.

The New York Times announced that Wordle is now playable within The New York Times Crossword app on Android and iOS. Players can access the popular word guessing game in the same app as three other games: The Crossword (the app's namesake), The Mini Crossword, and Spelling Bee.

https://twitter.com/NYTGames/status/1562470378483888130

It was, in a sense, ironic. Wordle was born from a husband's desire to make something fun for his partner. And for the better part of a half-hour this week, I managed to use it to cause a great deal of consternation for mine. That it was done inadvertently is of no matter.

Consider this a cautionary tale, then.

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wordplay, the crossword column

Jeff Chen and Jim Horne serve up a Friday puzzle.

By Isaac Aronow

FRIDAY PUZZLE — The two constructors of today’s puzzle, Jim Horne and Jeff Chen, are the creator and operator of the website XWordInfo , which is an important resource for crossword constructors. Without it, we might still be in the era of exclusively using dictionaries to fill grids. The clue and answer finder and the constructor directory are powerful tools that make finding granular information about crossword puzzles easy. If you haven’t checked out the site before, I recommend it.

As far as the grid goes, our constructors are no slouches, either. This is Mr. Horne’s third puzzle for The New York Times. All three have been collaborations with Mr. Chen, for whom this is his 123rd puzzle. It’s an astonishing number that ties him for 26th most prolific of all time, according to XWordInfo; the constructor he is tied with is Peter Gordon.

I’m a huge fan of this puzzle. It’s full of interesting and lively fill, such as 15A, 20A (which probably surprises nobody), 35A, 37A, 28D, 31D and 36D. That only covers what I don’t have listed below. So pick up your pencil, pen, phone, tablet or whatever you use to solve, and enjoy this gem.

Tricky Clues

1A. The clue, “Barrel of fun?” refers not to a barrel of monkeys but to a KEG.

21A. Neither the K-pop group BTS nor the Spice Girls: The “Super group” referenced here is the AVENGERS.

41A. Nice misdirect. I thought this would be something to do with stocks or bonds. The answer is actually MBAS, since many people in the corporate world “hold” the degrees.

51A. Another good misdirect, the “sweaters” in the clue refers not to the garment but to people who are sweating. The answer here is GYM CLASS.

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Encoded problem-solving procedure (maybe it’s time we let computers think for themselves, though? I dunno, just an idea) Crossword Clue

Encoded problem solving procedure maybe its time we let computers think for themselves though I dunno just an idea NYT Crossword Clue Answers are listed below. Did you came up with a solution that did not solve the clue? No worries we keep a close eye on all the clues and update them regularly with the correct answers.

ENCODED PROBLEM SOLVING PROCEDURE MAYBE ITS TIME WE LET COMPUTERS THINK FOR THEMSELVES THOUGH I DUNNO JUST AN IDEA Crossword Answer