Posts tagged ‘puzzle’

Is Your Gödel Too Tight?

I don’t care what Stevie Nicks says, thunder does not only happen when it’s raining. And sorry, Kelly Clarkson, I’m not standing at your door because I’m sorry.

Logical fallacies are rampant in song lyrics. (Don’t even get me started.) I’m therefore hopeful that you won’t attempt to channel your inner songwriter while trying to solve the following logic puzzles, arranged roughly in order of difficulty.

Here’s Looking at You

Jack is looking at Anne, and Anne is looking at George. Jack is married, George is not. Is a married person looking at an unmarried person?

Beer is Proof that God Loves Us

Three people walk into a bar, and the bartender asks, “Would all of you like a beer?” The first says, “I don’t know.” The second says, “I don’t know.” The third emphatically replies, “Yes!”

Why was the third one able to respond in the affirmative?

Five to the Third

A five-digit number is equal to the sum of its digits raised to the third power. Alphametically,

CUBED = (C + U + B + E + D)3

What is the five-digit number?

Martin Gardner’s Children

I ran into an old friend, and I asked about her family. “How old are your three kids now?”

She said the product of their ages was 36. I replied, “Sorry, I still don’t know how old they are.”

She then said, “Well, the sum of their ages is the same as the house number across the street.”

“I’m sorry,” I said. “I still don’t know how old they are.”

Finally, she told me that the oldest one has red hair, and I finally realized their ages.

How old are my friend’s children?

If At First You Don’t Succeed…

If you take a positive integer, multiply its digits to obtain a second number, multiply all of the digits of the second number to obtain a third number, and so on, the persistence of a number is the number of steps required to reduce it to a single-digit number by repeating this process. For example, 77 has a persistence of four because it requires four steps to reduce it to a single digit: 77-49-36-18-8. The smallest number of persistence one is 10, the smallest of persistence two is 25, the smallest of persistence three is 39, and the smaller of persistence four is 77.

What is the smallest number of persistence five?

The Hardest Logic Puzzle Ever

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

(This puzzle is attributed to Raymond Smullyan, but the twist of not knowing which word means which was apparently added by computer scientist John McCarthy.)


October 26, 2017 at 6:32 am Leave a comment

Number Challenge from Will Shortz and NPR

Typically, the NPR Sunday Puzzle involves a word-based challenge, but this week’s challenge was a number puzzle.

[This challenge] comes from Zack Guido, who’s the author of the book Of Course! The Greatest Collection of Riddles & Brain Teasers for Expanding Your Mind. Write down the equation

65 – 43 = 21

You’ll notice that this is not correct. 65 minus 43 equals 22, not 21. The object is to move exactly two of the digits to create a correct equation. There is no trick in the puzzle’s wording. In the answer, the minus and equal signs do not move.

Seemed like an appropriate one to share with the MJ4MF audience. Enjoy!

October 18, 2017 at 8:07 am 2 comments

Our Library’s Summer Math Contest

Every summer, our local library runs a contest called The Great Big Brain Game. Young patrons who solve all of the weekly puzzles receive a prize. The second puzzle for Summer 2017 looked like a typical math competition problem:

Last weekend, the weather was perfect, so you decided to go to Cherry Hill Park. When you got there, you saw that half of Falls Church was at the park, too! In addition to all the people on the playground, there were a total of 13 kids riding bicycles and tricycles. If the total number of wheels was 30, how many tricycles were there?


A tricycle has 3 wheels. (Duh.)

First, some comments about the problem.

  1. I dislike using “you” in math problems. I believe it’s a turn-off to students who can’t see themselves in the situation described. There are enough reasons that kids don’t like math. Why give them another reason to shut down by telling them that they went somewhere they didn’t want to go or that they did something they didn’t want to do?
  2. Word problems are not real-world just because they use a local context, and this one is no exception. This problem attempts to show an application for a system of linear equations, but true real-world problems don’t have all the information neatly packaged like this.
  3. Wouldn’t the person posing this problem already have access to the information they seek? That is, if she counted the number of kids riding bikes and the total number of wheels, couldn’t she have just counted the number of bicycles and tricycles instead? It has always struck me as strange when the (implied) narrator of a math problem wants you to figure out something they already know.

All that said, this was meant to be a fun puzzle for a summer contest, and I don’t mean to scold the library. I don’t know that I’d use this puzzle in a classroom — at least, not presented exactly like this — but I love that kids in my town have an opportunity to do some math in June, July, and August.

Now, I’ll offer some comments on the solution. In particular, the solution provided by the library was different than the method used by one of my sons. Here’s what the library did:

Imagine that all 13 kids were on bicycles with 2 wheels. That would be a total of 26 wheels. But since 30 wheels are needed, there are 4 extra wheels. If you add each of those extra wheels to a bicycle, that’ll create 4 tricycles, leaving 9 bicycles. So, there must have been 4 tricycles at Cherry Hill Park.

And here’s what my son did:

2017 Brain Game Puzzle 2

If you can’t see what he wrote, he created a system of two equations and then solved it:

2a + 3b = 30
a + b = 13

a + 2b = 17
13 – b + 2b = 17
b = 4

2a + 12 = 30
2a = 18
a = 9

That’s all well and good. In fact, it’s perfect if you want to assess my son’s ability to translate a problem and solve a system of equations. But I have to admit, I was a little disappointed. What bums me out is that he went straight to a symbolic algorithm instead of considering alternatives.

I think I know the reason for this. This past year, my son was in a pull-out math program, in which he studied math with someone other than his regular classroom teacher. In this special class, the teacher focused on preparing him to take Algebra II in sixth grade when he enters middle school. Consequently, students in the pull-out class spent the past year learning basic algebra. My fear is that they focused almost exclusively on symbolic manipulation and, as my former boss liked to say, “Algebra teachers are too symbol-minded.”

A key trait of effective problem solvers is flexibility. That type of flexibility comes from solving many problems and filling your toolbox with a variety of strategies. My worry — and this isn’t just a concern for my son, but for every math student in the country — is that students learn algorithms at the expense of more useful problem-solving heuristics. What happens when my son is presented with a problem that can’t be translated into a system of linear equations? Will he know what to do when he doesn’t know what to do?

The previous pull-out teacher said that when she presented my sons with problems that they didn’t know how to solve, their eyes would light up. They liked the challenge of doing something they hadn’t done before. I’m hopeful that this enthusiasm isn’t lost as they proceed to higher levels of mathematics.

July 14, 2017 at 7:00 am 2 comments

Friday Word Puzzle

Sometimes, a small word is contained in a longer word. For example, you can see the three-letter word rid tucked nicely inside Friday in the title for this post, and zip can be found in the middle of marzipan.

Some folks have told me that the following word-in-a-word is particularly appropriate for this blog…


…since my puns put the UGH in LAUGHTER.

Words within words are the basis of today’s puzzle.

Complete each of the nine words below by placing a three-letter word in the blank. The three-letter words that you use all belong to the same category. But there is a tenth three-letter word from the same category that is not used below. What is the category, and what is the missing word?

  1. OB _ _ _ D
  2. C _ _ _ PY
  3. M _ _ _ OT
  4. PH _ _ _ M
  5. H _ _ _ SE
  6. VE _ _ _ D
  7. CA _ _ _ OU
  8. EL _ _ _ SE
  9. LE _ _ _ E

When I started to create this puzzle, I was hoping to give you a similar list in which a short math word was found in a longer word. I found several, but they seem pretty darn hard, and the missing words aren’t always obviously mathy. But for fun, you can try your hand at these, too…

  1. D _ _ _ Y
  2. AS _ _  _ E
  3. SE _ _ _ H
  4. BU _ _ _ _ SS
  5. EL _ _ _ _ TH
  6. C _ _ _ _ RA
  7. RU _ _ _ _ NT
  8. SH _ _ _ _ BLE
  9. BRA _ _ _ _ ILD
  10. HU _ _ _ _ D
  11. PR _ _ _ _ _ IFY
  12. RE _ _ _ _ NT
  13. WA _ _ _ _ ELON
  14. DE _ _ _ _ OR
  15. HO _ _ _ _ SS
  16. H _ _ _ _ HOG
  17. IM _ _ _ _ ST



  1. OB eye D
  2. C hip PY
  3. M arm OT
  4. PH leg M
  5. H ear SE
  6. VE toe D
  7. CA rib OU
  8. EL lip SE
  9. LE gum E

The three-letter words are all parts of the body. The tenth word in that category is jaw, which never appears in the interior of a longer word (only at the beginning or end, such as jawbone or lockjaw).

  1. D add Y
  2. AS sum E
  3. SE arc H
  4. BU sine SS
  5. EL even TH
  6. C hole RA
  7. RU dime NT
  8. SH area BLE
  9. BRA inch ILD
  10. HU more D
  11. PR equal IFY
  12. RE side NT
  13. WA term ELON
  14. DE mean OR
  15. HO line SS
  16. H edge HOG
  17. IM mode ST

June 23, 2017 at 5:30 am Leave a comment

Dos Equis XX Math Puzzles

No, the title of this post does not refer to the beer. Though it may be the most interesting blog post in the world.


It refers to the date, 10/10, which — at least this year — is the second day of National Metric Week. It would also be written in Roman numerals as X/X, hence the title of this post.

For today, I have not one, not two, but three puzzles for you. I’m providing them to you well in advance of October 10, though, in case you’re one of those clever types who wants to use these puzzles on the actual date… this will give you time to plan.

The first is a garden-variety math problem based on the date (including the year).

Today is 10/10/16. What is the area of a triangle whose three sides measure 10 cm, 10 cm, and 16 cm?

Hint: A triangle appearing in an analogous problem exactly four years ago would have had the same area.

10-10-10 Triangle

The next two puzzles may be a little more fun for the less mathy among us — though I’m not sure that any such people read this blog.

Create a list of words, the first with 2 letters, the second with 3 letters, and so on, continuing as long as you can, where each word ends with the letter X. Scoring is triangular: Add the number of letters in all the words that you create until your first omission. For instance, if you got words with 2, 3, 4, 5, and 8 letters, then your score would be 2 + 3 + 4 + 5 = 14; you wouldn’t get credit for the 8-letter word since you hadn’t found any 6- or 7-letter words.

2 letters: _________________________
3 letters: _________________________
4 letters: _________________________
5 letters: _________________________
6 letters: _________________________
7 letters: _________________________
8 letters: _________________________
9 letters: _________________________
10 letters: _________________________
11 letters: _________________________
12 letters: _________________________
13 letters: _________________________
14 letters: _________________________

Note: There are answer blanks above for words up to 14 letters, because — you guessed it — the longest English word that ends with an X contains 14 letters.

The third and final puzzle is a variation on the second.

How many words can you think of that contain the letter X twice? (Zoiks!) Scoring: Ten points for the first one, and a bazillion points for each one thereafter — this is hard! Good luck!

If you’re in desperate need of help, you can access my list of words for both puzzles — of which I’m fairly proud, since my list of words that end in X include math words for 2 through 10 letters — or do a search at

October 6, 2016 at 10:10 am Leave a comment

AWOKK, Day 7: KenKen Puzzle for 2016

Good day, and welcome to Day 7 of the A Week of KenKen series. If you’ve stumbled onto this page randomly, you should definitely check out some of the fun we’ve had previously…

Well, here it is, September 25, a mere 269 days into the year, and I am only now presenting you with a KenKen puzzle based on the year. I suppose I can take some solace in the fact that I’m presenting the following 2016 KenKen puzzle before the year is over. Little victories.

You might note that the puzzle has the following attributes:

  • The numbers 2, 0, 1, and 6 are featured prominently as individual cells.
  • Every target number uses (some combination of) the digits 2, 0, 1, and 6.
  • There are two large cages — one in the shape of a 1, the other in the shape of a 6 — each with a product of 2016.

This puzzle follows the standard rules of KenKen, but there is one major exception: although it is an 8 × 8 puzzle, instead of using the digits 1‑8, it uses 0‑7.

KenKen 2016 Puzzle

If you’re stuck, just fill in the squares randomly. There are only 108,776,032,459,082,956,800 different Latin squares of size 8 × 8, and your chances of guessing correctly are even better since 4 cells are already filled in.

As it typical of all puzzles presented on this blog, I am not posting the solution. At least, not yet. Maybe someday. If you beg. Or send me money. But not today.

September 25, 2016 at 5:05 am Leave a comment

AWOKK, Day 6: KenKen Glossary

KENgratulations! You’ve made it to Day 6 of MJ4MF’s A Week of KenKen series. If you happened to miss any of the fun we’ve had previously…

Robert F. Fuhrer is a toy inventor with a knack for coming up with creative names, including Crocodile Dentist, Gator Golf, T.H.I.N.G.S. (Totally Hilarious, Incredibly Neat Games of Skill), Rumble Bugs, Missile Toe (literally, a rocket in the shape of a toe), and many others. As the president of Nextoy, LLC, which holds the registered trademark for KenKen®, Bob now uses his creative naming abilities for the appellations of KenKen-related products.

The word that started this post, KENgratulations, is just one of his many linguistic creations. I rather like the term he coined to describe the computer application that randomly generates KenKen puzzles.

KEN·er·tor n. the “machine” (computer application) used to automatically generate KenKen puzzles

Quick! We need more 6 × 6 puzzles. Crank up the Kenerator!

The name conjures images of a machine from Willy Wonka.

Oompa, loompa, doom-pa-dee-do,
I’ve got a perfect puzzle for you…

Numbers and operations go in, puzzles come out.

The Kenerator

Bob can also take credit for the following:

KEN·cil n. a pencil used to solve KenKen puzzles

I prefer kencils rather than pens when solving KenKen puzzles.

KEN·grat·la·tions n. an expression of praise for solving a KenKen puzzle

Kengratulations for solving that puzzle in less than 7 years!

KEN·thu·si·ast n. someone who likes to solve KenKen puzzles

Most Kenthusiasts solve more than one KenKen puzzle a day.

There’s no doubt, Bob is good. But as you saw in a previous post, I’ve got a knack for coining terms, too…

KEN·tath·lon n. competition involving multiple KenKen events

I complete a Kentathlon consisting of a 4 × 4, 5 × 5, and 6 × 6 puzzle every morning.

e·go·KEN·tric adj. a person who thinks that they are better than others at solving KenKen puzzles

He’s completely egokentric, even though he’s never won a KenKen tournament.

KEN·tral of·fice n. where KenKen puzzles are made

The Kenerator resides in the kentral office.

KEN·te·nar·i·an n. person who has solved 100+ KenKen puzzles

He became instantly addicted to KenKen puzzles; he became a kentenarian in less than 3 weeks.

su·per·KEN·te·nar·i·an n. person who has solved 100+ KenKen puzzles in one day

She became a superkentenarian by completing all the puzzles in Ferocious KenKen on Saturday.

KEN·ta·gon n. the arena in which KenKen tournaments take place (analogous to the Octagon, the eight-sided chain-link enclosure used for Ultimate Fighting Championship matches, though usually less violent)

Enter the kentagon, prepare to solve!

KEN·o·pause n. the period in a puzzle solver’s life when KenKen ceases to be fun

Kenthusiasts who have entered kenopause usually solve fewer than one puzzle a day, on average.

KEN·i·ten·tia·ry n. where KenKen solvers are locked up if they’re caught cheating (syn prism)

If you copy off your neighbor at a KenKen tournament, you’ll be sent to the kenitentiary.

KEN·al·ty n. a disadvantage imposed on a puzzle solver at a tournament for an infringement of the rules

He was given a 15-second kenalty for “using a kencil in an unsafe manner.”

KEN·ais·sance n. the period from roughly 2008 to 2010 when KenKen puzzles experienced tremendous growth in popularity, likely the result of publication in The Times (London), the NY Times, and other newspapers

Harold Reiter’s interest in KenKen started long before the Kenaissance.

KEN·der·foot, n. an amateur; someone who has solved only a few KenKen puzzles

He’s such a kenderfoot; he doesn’t even know the X-wing strategy!

KEN·den·cies n. the habits of a KenKen solver; analogous to a “tell” in poker

He has a kendency to complete all of the addition cages before attempting any subtraction cage.

hy·per·KEN·ti·late n. to breathe heavily while solving a puzzle (usu., a result of having difficulty)

At the 2013 KenKen International Championship, she started to hyperkentilate when she had trouble with a difficult 6 × 6 puzzle.

September 24, 2016 at 5:05 am Leave a comment

Older Posts

About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.

Past Posts

November 2017
« Oct    

Enter your email address to subscribe to the MJ4MF blog and receive new posts via email.

Join 297 other followers

Visitor Locations

free counters