Is there a word for this type of brainteaser?

Miscellaneous and Personal Stuff I Must Share
1

I saw this on Facebook. It seems easy but seems to fool people:

“I bought a reindeer for $900 and sold it for $1300. I bought it back for $1400 and sold it for $1700. What profit did I make?”

The answer is $700, which seemed obvious to me, but it REALLY throws people. the most common answer is $600, which is demonstrably wrong, but you can kind of understand why people get that; they seem to assume buying another product for $100 more than the first sale price means a loss and they tend to double count that $100.

It reminded me of a very famous old riddle; three men check into a hotel. They are charged $30 for a room they will share, so each pays $10. The desk clerk realizes he erred and the room was only $25, so he gives a bellboy $5 in singles to give back to the men. The bellboy says the hell with it, tells them it was $27 and gives each $1 back, keeping $2 for himself. Since each man has now paid $9, 3x9 is 27, and the bellboy has $2, and 27+2 is 29, where’s the missing dollar? The answer is there isn’t one. The men spent $27, $25 on the room, $2 to the thieving bellboy. You can’t add 27 to 2 at all. The 2 is PART of the 27.

Both these riddles rely on confusing you by making unrelated numbers seem related. In Riddle 1, the reindeer being sold for $1300 and repurchased for $1400 makes you think that $100 difference matters, but it’s not a relevant number at all. (The illusion is swiftly broken if you just charge the wording to say it’s two different reindeer, or two totally different products, as one might buy in a store.) The second problem tricks you into counting a number twice.

Another similar riddle; a thief enters a store. He steals $100 from the register. He then uses the $100 to purcahse a $70 item, and leaves with the item and $30 in change. How much did he steal? Clearly, he stole $100 - an accountant will tell you it’s absolutely just $100 cash, that no goods were stolen, and she’d be right, but if you want to insist it’s $30 in cash and $70 in goods I won’t bother arguing, because the amazing thing is many people will SWEAR the thief stole $200, $130, or $170.

Is there a word for this type of math puzzle - a puzzle where the arithmetic is actually simple but the wording and closeness of numbers can throw people?

Know any others?

2

I don’t know an official name for it…we called them word problems in 5th grade.
I know I hated the hell outta them.

3

I see some mentions calling them wordy math problems.

4

Idiot sold it the first time for way too little. Should have held out till that second buyer came around, and he would have made $800!

5

They’re sometimes called paradoxes.

6

Inaccurately, in my view. A paradox is an actual contradiction in terms, these are just obfuscation.

I posted something along these lines a few years ago, that actually happened to me. The short version is, I was in a casino and placed a £100 bet on roulette, on red. The ball landed in a black number on that spin, but for whatever reason, the croupier didn’t clear my chip from the table. I left it there for the next spin, which came up red, and the croupier paid my winnings of £100, at which point I took £200 off the table, cashed out, and left. How much did I ‘steal’ from the casino? The responses were very interesting, but the only ones I totally rejected were those that suggested I had stolen £200.

7

Yes, they’re more often just called riddles.
IMHO, regarding the casino scenario, you appear to have $200 which you shouldn’t
(morally) have…

8

Had - I’ve been back many times since! :slightly_smiling_face:

ETA: the reason I reject that notion is I could have placed a further £100 bet for the second spin, with my own money. I didn’t need to thanks to the initial oversight, but I’m only up £100 on the transaction.

Dont want to relitigate it all here, someone less lazy than me should be able to find the thread (I started it) if they want to bump it.

9

I just ask the Lil’wrekker. Closer to grade school math than I am.
She said one of her teachers called them Story problems .

And, yes she hated them as well.

10

Suppose that @Dead_Cat had picked up the $100 worth of chips after the dealer failed to collect them, and put them in their pocket. And suppose that they then put another $100 worth of chips back down on the table in preparation for the next spin. How is that any different from what did happen?

Alternately, suppose that @Dead_Cat had taken all of the same actions, but had lost the second spin, and this time the dealer collected the chips as they were supposed to. @Dead_Cat walks away empty-handed. Would you say in this case that they didn’t steal anything, since they walked away without it?

(and of course, the real answer is that they didn’t steal anything, because it was the casino’s responsibility to collect the losing chips, not the player’s)

11

I think this is what you said in the original thread: Moral dilemma - gambling related

13.5 years ago, man. Please could we move this hijack to there? Apologies to the OP.

12

I LOVED word problems. Usually there were 20 or 25 problems on a homework page, but when there were word problems-- we called them “story problems”-- there’d be 4 or 5. Too easy.

While the puzzles are technically story/word problems, I think they are more than that. The kind of story problem in my math book was always straightforward-- Sue has 5 apples, and she gives 1 apple to Lou. How many apples does Sue have left?

The tricky problems the OP is presenting may require arithmetic, but they are logic puzzles.

When story problems and logic puzzles meet on the Venn diagram, these are what you have.

The Monty Hall problem is similar, in that while it doesn’t have mathematical terms in the story, it requires some basic math to get to the answer, but also the insight that Monty knows where the prize is, and never opens a door with the big prize.

This problem somehow is the Ur problem like this-- I mean, it can’t really be, since these have to go back before Monty Hall, but this seems to be the one everyone knows, and so they are actually referred to as “Monty Hall problems.”

If you define a Monty Hall problem as a “brainteaser with math,” then I’d call this one.

13

You are missing the point in both of your replies. He wasn’t asking what word problems are called, he was asking what word problems with tons of irrelevant information designed to be confusing are called.

14

Hah.

Since Dead Cat just picked up stray chips, and didn’t threat or coerce money from anyone, I wouldn’t call it theft.

Here’s a problem:

I was 11 when I was at the arcade of a ski resort with a friend, and we spotted two $50 bills on the floor and picked them up and pocketed them, did we steal?

I don’t think so.

But that isn’t the end of the story.

About 10 minutes later, we saw a couple clearly looking for something, and mostly over in the place where we had found the money.

If we kept it art that point, is it theft?

We thought it was, and asked the couple if they lost something (we didn’t say what). They said $100 in 2 fifties, and at that point we returned the money. The couple gave us each a $20. $20 guilt-free dollars.

15

There has been a Straight Dope column about this one.

Not really the same kind of puzzle, I don’t think, but it has in common that it misleads people with irrelevant numbers and irrelevant calculations:

16

I once tried combining a word problem and a pun with ChatGPT:

17

As I was going to St. Ives
I met a man with 7 wives
And each wife had 7 sacks
And each sack held 7 cats
And cat had 7 kits
Man, wives, sacks, cats, kits
How many were going to St. Ives?

One. As I was going to St. Ives

18

Sure it matters. Suppose you ignored that intermediate transaction completely: you bought the reindeer for $900 and sold it for $1700. Is that $800 in profit?

No, because you lost $100 in the middle. Subtract that from $800, and you get the correct $700.

19

I don’t know a general term, but one might call them “decoys” since they tend to include extraneous or misleading details that may confuse many.

20

Perhaps you met at a junction coming from different directions, but all turning toward St Ives. Perhaps you caught up with them while they were having a rest before continuing on their journey to St Ives. And we always need to know how many kittens there are to make sure we don’t lose one.