Posted by: tejat | December 5, 2008

Some More (Tricky) Brainteasers!

Sooo… I really like brainteasers, and I can’t figure these out, so I figured I might as well share my frustration with the class!

Here’s the first one– It’s kind of weird, and I feel like there’s some trick you’re supposed to pick up on:

Two old friends, Joel and Fred, run into each other on the street. It’s been a while since they’ve had a chance to catch up. They have the following conversation:

Joel: Hey! How’ve you been?
Fred: Great. I’m married and have three daughters.
Joel: That’s great news. How old are they?
Fred: The product of their ages is 72.
Joel: Right. Hmm. I can’t figure it out.
Fred: Okay. The sum of their ages is the same as that building’s address.
Joel: Okay… Nope. I still don’t know.
Fred: Oh. Sorry. The oldest one has red hair.
Joel: Oh great. My oldest is the same age.

How old are the daughters?

Any ideas?

The second is a bit more mathy– I’m not sure if anyone has ever played the game “24” (like in elementary school), but it’s a game where you have 4 numbers and have to manipulate them to get the number 24. You may add, subtract, multiply and divide, but you must use each number once and only once. For example, if the numbers were 3, 4, 5 and 12, I could say 3+4 is 7, 7-5 is 2, and 2*12 = 24. That was easy. This one is hard. Or maybe not but I’m just having the hardest time figuring it out, as is everyone else I know. The numbers are, (drumroll…) 6, 4, 3, 1.  It definitely has a solution, I just can’t figure it out. Go for it!


  1. 2*6*6 (14)
    3*3*8 (14)

    This leaves us only two possible options.
    Then we are told that the oldest had red hair. This means there is an oldest so we can eliminate 2*6*6 because there is no oldest here.
    So the answer is 3,3,8.

    As for the second question. I definitely remember doing this in high school. 6/(1-3/4)

  2. hmm I definitely typed out a full response to the first question but I dont know what happened to it and dont feel like typing it all out. The idea is you figure out all the combinations that multiply to 72 and then you find all of the sums of the ages. Then you eliminate all the unique sums because even knowing the sum didnt tell the guy the answer. This leaves only 14 as the sum

  3. Oh, 24! I am pretty bad at that game, but we played it all the time in math camp in the summer (yes, I went to math camp in high school — it’s called PROMYS, it’s held here in Boston, and I learned lots of the stuff you guys are doing in Math 152 for the first time while I was there (modular arithmetic, spherical geometry, polynomial rings…))

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