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!”