Some More Math/Logic Problems To Test Your Wits

I got a surprising amount of emails about this post, with requests for more such puzzles, so here you go (answers after the jump).

1. A deaf-mute man walks alone up to a movie theater counter shortly before a matinee which costs 50 cents to enter. Making no particular gesture (and obviously, saying nothing), he hands the clerk a dollar. Rather than giving him 50 cents in change, the clerk hands him two tickets. The man smiles and nods his thanks. How did the clerk know that he wanted two tickets rather than one?

2. Four people are fleeing the zombie apocalypse in the dark of night, and have to get across a narrow bridge in 17 minutes to survive. The bridge is so rickety that no more than two people can stand on it at any one time or it will collapse. It is also full of holes such that it can only be safely crossed while holding a flashlight. The 4 people have only one flashlight between them. A further challenge is that the 4 people are of different ages and levels of health, such that it takes each a different amount of time to cross the bridge. One takes 10 minutes, one needs 5 minutes, one needs 2 minutes, and one needs 1 minute (all invariably, i.e., no amount of help from a faster person can speed a slower person up). How do the 4 people manage to save their lives by crossing their entire party in the 17 minutes available?

3. A man with a heart condition has to take two medications at the same time every 4 hours or he will die. The medication regime is hard to follow: If he takes none or just one of the needed pills at the appointed time, or he takes that more than 1 of either pill within each 4 hour block, he will have a fatal heart attack. To add to the complexity, the pills of each medication are exactly the same in every respect – color, shape, size, texture, weight, labeling. He copes with this challenge by keeping each medication in its own, clearly labelled pill bottle.

While at his hunting lodge in Northern California, something terrible happens. Just before he is about to take his medications, a earth tremor hits and he falls over. The tremor passes quickly, but unfortunately all but 2 pills have fallen out of one bottle and all but 3 have fallen out of the other. Every other pill is scattered on the floor and he can’t tell them apart! It’s a two day trip back to town where he can help from his pharmacist and doctor, and he has no phone, so he has to figure out how to keep himself alive until he can return to town. How does he do it?

4. 4. A man hands a bank teller a check with the symbols “O – O X +” written on the back. The teller says “Oh, I see you are in the navy!”. Why?

1. The man gave the clerk 4 quarters, so the clerk knew he wanted two tickets rather than 1 ticket and 50 cents in change.

2. The 1 minute and 2 minute walkers go over first together (2 minutes elapsed)
Then the 1 minute walker returns with the flashlight (3 minutes elapsed)
Then the 10 and 5 minute walkers cross together (13 minutes elapsed)
Then the 2 minute walker brings back the light (15 minutes elapsed)
Then the 1 minute and 2 minute walkers cross together (17 minutes elapsed)

3. Count the total number of pills and divide by 2, getting the number of remaining doses (call it X). Gather all the pills and grind and mix them into a bowl. Take one Xth of the mixture every four hours until safely back in town.

4. The man was wearing his uniform!

Author: Keith Humphreys

Keith Humphreys is the Esther Ting Memorial Professor of Psychiatry at Stanford University and an Honorary Professor of Psychiatry at Kings College Lonon. His research, teaching and writing have focused on addictive disorders, self-help organizations (e.g., breast cancer support groups, Alcoholics Anonymous), evaluation research methods, and public policy related to health care, mental illness, veterans, drugs, crime and correctional systems. Professor Humphreys' over 300 scholarly articles, monographs and books have been cited over ten thousand times by scientific colleagues. He is a regular contributor to Washington Post and has also written for the New York Times, Wall Street Journal, Washington Monthly, San Francisco Chronicle, The Guardian (UK), The Telegraph (UK), Times Higher Education (UK), Crossbow (UK) and other media outlets.

2 thoughts on “Some More Math/Logic Problems To Test Your Wits”

  1. In scenario #2, sadly, at least one and possibly two of the people are lost, since it takes at least a minute to work that whole system out, and then they're going to lose several more minutes explaining it to the one who doesn't get it and really thinks they need to understand the whole thing before anyone tries crossing the bridge and the other one who thinks they should be in charge and either doesn't have it worked out or has it worked out wrong but who mostly just wants to be acknowledged as being in charge. I refrain from pointing out the additional loss of time if the person who works it out while they're getting to the bridge is the plucky intern, or (if the group is American) female, pretty, Black or Hispanic, or an athlete, and one of the others is a politician, a CEO, a management consultant, a retired military officer of flag rank or really just anyone who thinks they should be the one giving the orders and who keeps talking over the person who actually worked out the system. And then, of course, there's the person who used to be in pretty good shape and thinks he's the 2-minute person but isn't.

    No, they're definitely going to need more time. A lot more time.

  2. I don't love 1 and 4, because they depend pretty explicitly on misdirection. It makes me think of some of my 9-year-old's riddles, which depend on some item extraneous or contradictory to the text of the riddle for the answer. But I admit that's just a personal preference. If the text of 1 read "… hands the clerk $1.00…" it would be much less garden-path, but perhaps too obvious.

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