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Puzzles, Teasers and Problems

Presented here are some favorite brain stretchers. Until it becomes too time-consuming, I will acknowledge solutions e-mailed to with confirmation of correct answers and encouragement to keep trying--or possibly hints (don't hold your breath)-- for incorrect ones.

The Problem

Comments on the problem

Given 8 apparently identical balls and a 2-pan balance (scale), find the one ball that weights a tiny bit less by using the scale only twice.

A trial-and-error approach will work here, there being a limited number of possible combinations.

 Given ten stacks (each containing ten nickels and each minted in a different year), find the stack in which each nickel weighs only 4 grams instead of the usual 5 grams. You may use a scale that reads in grams, but you may take only a single reading from it.

 I don't know anyone who has solved this one who could describe the thought process by which the solution was reached. Just about everyone says something like, "It just came to me to..."

The cat had kittens. I gave half of them, plus half a kitten to my brother. Then I gave half of the remainer, plus half a kitten to my sister. No kittens were harmed and I still have one kitten. How many kitted did the cat have?

Remember: no kittens must be harmed. 

How many pets do I have if all but two of them are dogs, all but two of them are cats, and all but two of them are hamsters?


Gloria is new in town. She has a job, but no paycheck until the end of the week. She has enough cash for food, but not for lodgings. She does have a heavy gold bracelet in the form of a chain of seven links. She and the hotel clerk agree that each link is worth about the price of a night's lodging. Since he won't trust her to pay at the end of the week, she doesn't want to turn the whole bracelet over to him. She decides to have a jeweler cut the bracelet so she can pay for each night as it comes. She wants to pay the jeweler to make the fewest possible number of cuts (and solders later to restore the bracelet). How should she tell him to cut the links?

This one comes from Martin Gardener's puzzle collection called "Aha!"

Ruth left home running, then turned left, ran on, turned left again, ran yet farther, turned left once more and ran toward home. Two masked men were waiting there. Who were they?

In Arkansas why can't you take a picture of a pregnant woman with a wooden leg?

Given 50 apparently identical coins and a 2-pan balance (scale), find the one coin that weights a tiny bit more by using the scale no more than four times.

Solving the puzzle about the eight balls will provide useful insight into this one.

Do you like puzzles? Try the Case Studies for more involved problems
with a biological emphasis and insight into thinking like a scientist.

Two National Public Radio programs challenge listeners once each week with
puzzles. There may be several hundred people who succeed, so a drawing
determines who wins the modest prizes offered.

The prize on Weekend Edition Sunday Morning includes the chance to solve a
series of related puzzles on-air. The link here takes you to the page where the
current puzzle is stated along with past weeks' puzzles and solution plus an
e-mail link to submit a solution (by close of business Thursday).

Also check out Tom & Ray's Car Talk puzzler page:
If you send a correct and timely answer to their most recent
puzzle you can be eligible to win a prize (a gift certificate
usable in their Shameless Commerce Department).

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