## Posts tagged ‘logic’

### IDK Puzzles

I like logic, and I like beer, so it’s no surprise that this is one of my favorite online comics:

Not sure why that’s funny? There’s an explanation at www.beingamathematician.org.

Logic puzzles in which a protagonist states, “I don’t know!” are ubiquitous. Borrowing from texting culture, I’ve taken to calling these IDK Puzzles.

Every math person remembers the first non-routine problem they solved and, more importantly, the *feeling* they experienced when solving it. The first time I had that feeling occurred after solving a logic puzzle about three children’s ages that I discovered in a Martin Gardner book; now many years later, I don’t remember the title of the book, and the following is my best recollection of the puzzle:

Two neighbors are speaking. One asks the other, “I know you have three children, but how old are they?”

The other says, “The product of their ages is 72.”

The first neighbor says, “I still don’t know their ages.”

“Well,” says the other, “the sum of their ages is equal to our street address.”

The first neighbor again replies, “I still don’t know their ages.”

“I’m sorry,” says the other, “I can’t talk anymore, because I have to take my oldest child to the dentist,” and then leaves.

While saying good-bye, the first neighbor thinks, “Ah, now I know their ages.”

This puzzle is typical of the genre, in that it appears there is insufficient information, but those who persist will be rewarded. Can you figure out the three children’s ages?

A slightly different IDK Puzzle involves geometric shapes.

Two people are shown the following five shapes:

They are told that a prize has been placed under one of the shapes. One of the people is told the color, and the other is told the shape, but they are not allowed to share their information with each other.

They are asked, “Do either of you know where the prize is hidden?”

Both of them reply, “I don’t know.”

They are asked a second time, “Do either of you know where the prize is hidden now?”

Again, they both reply, “I don’t know.”

They are asked a third time, “What about now?”

They both reply, “Yes!”

Under what shape has the prize been hidden?

Enjoy solving those puzzles. Staying with the theme, let’s end this post with a logic joke of sorts…

Sam comes home from the grocery store with twelve gallons of milk. Pam asks, “Why’d you buy so much milk?”

“Because before I left, you told me to buy a gallon of milk, and then you said, ‘If they have eggs, buy a dozen.’ And they had eggs.”

Pam shakes her head at Sam’s response. But then she notices he hasn’t bought anything else and asks, “Where are the rest of the things we needed?”

“Remember how you told me to put ketchup on the list?” replies Sam.

“Yeah. So?”

“So I put ketchup on the list, but then I couldn’t read the other items!” Sam says. “But I remembered the eggs!”

### 2017 KenKen International Championship

If you like puzzles and ping pong, then Pleasantville, NY, was the place to be on December 17.

More than 200 Kenthusiasts — people who love KenKen puzzles — descended on Will Shortz’s Westchester Table Tennis Center for the 2017 KenKen International Championship (or the KKIC, for short). Participants followed 1.5 hours of solving KenKen puzzles with a pizza party and several hours of table tennis.

The competition consisted of three rounds, with the three puzzles in each round slightly larger and more difficult than those from the previous round. Consequently, competitors were given 15, 18, and 20 minutes to complete the puzzles in the first, second, and third rounds, respectively.

Competitors earned 1,000 points for each completely correct puzzle, and 0 points for an incomplete or incorrect puzzle. In addition, a bonus of 5 points was earned for every 10 seconds in which a puzzle was turned in before time was called. So, let’s say you got two of the three puzzles correct and handed in your answers with 30 seconds remaining in the round; then, your score for that round would be

The leader after the written portion was John Gilling, a data scientist from Brooklyn, whose total score was 10,195. And if you’ve been paying attention, then you know what that means — Gilling earned 9,000 points for completing all of the puzzles correctly, so his time bonus was 1,195 points… which is the amount you’d earn for turning in the puzzles 2,390 seconds (combined) before time was called. The implication? Gilling solved all 9 puzzles from the written rounds — which contained a mix of puzzles from size 5 × 5 to 8 × 8 — in just over 13 minutes.

Wow.

As a result, Gilling, the defending champion, earned a spot in the Championship Round against Tess Mandell, a math teacher from Boston; Ellie Grueskin, a high school senior at The Hackley School; and Michael Holman, a technology consultant. In the final round, each of them attempted a challenging 9 × 9 puzzle, which was displayed on an easel for the crowd to see. Solving a challenging 9 × 9 is tough enough; having to do it as 200 kenthusiasts follow your every move is even tougher.

So, how’d they do? See for yourself…

When the dust settled, Gilling had successfully defended his title. For his efforts, he received a check for $500. But more importantly, he retained bragging rights for one more year.

If you think you’ve got what it takes to compete with the best KenKen solvers, try your hand at the 9 × 9 puzzle that was used in the final round. In the video above, you saw how fast Gilling solved it to win the gold. But even the slowest of the four final-round participants finished in under 15 minutes.

Again, wow.

Finally, I’d be failing as a father if I didn’t mention that my sons Alex and Eli competed in the Delta (age 10 and under) division. Though bested by Aritro Chatterjee, a brilliant young man who earned a trip to the 2017 KKIC by winning the UAE KenKen Championship, Eli took the silver, and Alex brought home the bronze. They’re shown in the photos below with Bob Fuhrer, the president of Nextoy, LLC, the KenKen company and host of the KKIC.

#proudpapa

For more KenKen puzzles, check out www.kenken.com, or see my series of posts, A Week of KenKen.

### 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,

*CU**BED* = (*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.)

### Insanity, the Logic of a Mind Overtasked

I asked my friend what he knew.

I don’t know anything.

Who are you, the Barber of Seville? You know at least one thing, namely that you don’t know anything. A contradiction!

So he corrected himself.

I don’t know nothing.

Ha! If you don’t (-) know nothing (-), then you must know something (+). A double negative.

It was at that point that my friend stopped being my friend.

This is what logic will do to your social life.

Logic: a systematic method for getting the wrong conclusion, with confidence.

But it can also be useful for solving problems.

John had 50 candy bars, and he ate 45 of them. Now what does he have?

Diabetes!

And we end this silliness with three pieces of advice from the king of bad logic, Yogi Berra.

- Never answer an anonymous letter.
- Nobody goes there anymore. It’s too crowded.
- You better cut the pizza in four pieces. I’m not hungry enough to eat six.

Hope you enjoyed or did not enjoy this post (but not both).

### Can’t Argue with That

My momma always told me:

Don’t break a person’s heart; they only have one. Break their bones; they have 206.

Who can argue with that logic? Here are some other logical statements with which you won’t want to argue, either.

I asked my wife what she wanted for her birthday. She said, “Nothing would make me happier than diamond earrings.” So, I got her nothing.

I find it strange that my advisor always begins conversations with me by saying, “You haven’t heard a word I’ve said, have you?”

It doesn’t matter if the glass is half empty or half full; either way, there is room for more alcohol.

I only drink twice a year: when it’s my birthday, and when it’s not.

My math teacher just fell in a wishing well. Go figure! I never knew they worked.

My advisor says I’ll never graduate because I’m lazy. But I just can’t take that kind of criticism. I was going to kill myself… but the gun’s, like, way over there.

Don’t judge a book by its cover… my math book has a picture of someone enjoying himself.

A grad student told his friend, “My girlfriend hates it when I sneak up behind her and kiss her on the cheek. But according to her lawyer, she also hates it when I call her my girlfriend.”

I got a tattoo of Chinese symbols on my arm that reads, “I don’t know. I don’t speak Chinese.” So when someone asks what it says…

Boy: I hate my math professor. He’s a terrible lecturer, he has bad breath, and he laughs at his own jokes.

Girl: Who’s your professor?

Boy: Dr. Jacoby.

Girl: Do you know who I am?

Boy: No.

Girl: I’m Dr. Jacoby’s daughter.

Boy: Do you know who I am?

Girl: No.

Boy: Good.

### Silly-Gisms

A *syllogism* is a logical argument in which the conclusion is inferred from two premises. As an example:

All men are animals.

All animals are mortal.

Therefore, all men are mortal.

My favorite syllogism comes from comedian Richard Geni who delivered the following in one of his stand-up routines:

Love is blind.

God is love.

Therefore, Ray Charles is God.

Here are a few other syllogisms that are a little more mathematical, though equally silly.

Ten percent of all car thieves are left-handed.

All polar bears are left-handed.

If your car is stolen, there’s a 10% chance it was taken by a polar bear.Thirty-nine percent of unemployed men wear glasses.

Eighty percent of employed men wear spectacles.

Therefore, work causes bad vision.Every second, 4,000 cans are opened around the world.

Every second, ten babies are conceived around the world.

Therefore, each time you open a can, you have a 1 in 400 chance of becoming pregnant. (Be careful!)

### There Must Be Some Misunderstanding

The WordPress blogging system comes with administrative controls, and it allows me to see what folks are searching for when they reach my blog. One of the search phrases that showed in the admin area today:

“math jokes – if you get them, you don’t have friends”

That’s not true. And I can prove it’s not true, by showing that its contrapositive is untrue.

P = You get math jokes.

Q = You have friends.

Then this argument is

If P, then -Q.

The contrapositive is, “If you have friends, then you don’t get math jokes.” Symbolically,

If Q, then -P.

I have friends. Or, I have at least one friend, which is all I need to prove the truth of Q. And given that I’m the author of this blog, then clearly I get math jokes. Consequently, the contrapositive is untrue; and by the Law of Contrapositives, then the original statement is untrue. Q.E.D.

Sticking to formal logic, Brent Yorgey recently reviewed Math Jokes 4 Mathy Folks on his blog The Math Less Traveled. In his review, he stated that this was one of his favorite jokes in the book:

A logician said to his son, “If you don’t eat your vegetables, you can’t have any ice cream.” Upon hearing this, the son choked down a plate of broccoli, and his father, duly impressed, sent him to bed without any ice cream.

Upon reading this review, my publisher said, “What a terrible joke he chose to highlight! I don’t understand why it’s funny. The logician just sounds cruel!”

I then had to explain that the humor derives from the logical error known as denying the antecedent. The logician said, “If you don’t eat your vegetables, then you can’t have any ice cream.” It is a common mistake for folks to assume that the logician’s statement is equivalent to, “If you eat your vegetables, then you can have ice cream.” But it’s not. The second statement is the inverse of the original statement, and a statement and its inverse are not logically equivalent. The logician asserted that if the son didn’t eat the vegetables, then he would not get ice cream; however, he did not guarantee that his son would get ice cream for eating his vegetables.

Yeah, you’re right. Even if you understand it, it’s still not very funny.

### Three Jokes from Italy

Thanks to Maurizio Codogno, who bought my book from bookdepository.co.uk (they were kind enough to ship it to him in Italy), and who also shared a few jokes that weren’t in *Math Jokes 4 Mathy Folks*. Enjoy them, hot off the presses from Milan!

**Question and Answer**

Q: What is the difference between a mathematician and a physicist?

A: The mathematician thinks there is only one straight line that passes through two points; the physicist, however, needs more data.

**Logic Exam**

A student asks his logic professor, “Sir, did I pass or fail the exam?”

The professor replies, “Yes.”

**Quantum Mechanics**

Every Friday night, a mathematician goes to the pub, sits on the next-to-last stool, turns to the last stool, and asks to a non-existent woman if she would like a drink. The mathematician returns every Friday night for a year, yet the bartender says nothing.

Finally, the last Friday before summer break, the bartender asks the mathematician, “Excuse me, sir. You are clearly aware that there is no woman sitting in that chair. Why do you keep talking to an empty stool?”

The mathematician responds, “According to quantum mechanics, an empty space is not really void. Virtual particles materialize and disappear at every instant. Nobody knows whether the appropriate wave function collapses in such a way that a beautiful girl will appear out of nowhere.”

The bartender raises his eyebrow. “Really? That’s interesting. But couldn’t you just ask one of the women already in the bar if she’d like a drink? Who knows, maybe one of them would say yes.”

The mathematican laughs. “Oh, sure!” he says. “And what is the probability of

thathappening?”