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Easy to visualize but challenging to solve: that's the kind of math puzzle you get here, one per episode. (Do you love the Car Talk Puzzler too? Yeah, that's what I'm trying for here, only with even more of a math bent.)
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A parking lot has 16 spaces in a row. Twelve cars arrive, each of which requires one parking space, and their drivers choose their spaces at random from among the available spaces. Santa Claus then arrives in his oversized and very full sleigh, which requires two adjacent spaces. What is the probability that there’s a place for him? // Spiciness: *…
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Last week, two of my friends and I went to a restaurant and had a lovely meal. We decided to evenly split the check, so we asked the waiter to just combine the totals. However, when the waiter came with the check, he revealed that there had been a mistake and instead of recording the complete total, the computer only returned a list of the totals o…
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A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token into a discard pile. The game ends when some player runs out of tokens. Players A, B, and C start with 15, 14, and 13 tokens, respectively. // How many rounds will there …
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Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. // What is the length of the track in meters? // (Also, a challenge for all lis…
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My perpetually tricky friend told me that while she was walking through town she saw four particularly vibrant houses. There was an auburn one, a brick one, a cherry one, and one the shade of dogwood rose. She wanted me to figure out the order of the houses. She said that the the auburn came before the the brick one while the cherry one came before…
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A friend of mine told me that she can walk a mile south, a mile east, a mile north and end up back home. I first thought she lived at the north pole, but she laughed and told me that, since there was no land there, she would be unable to make the walk. She asked me to try again, so I thought for a few minutes before finally saying that I knew how t…
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Working alone, I put two coats of paint on a wall, one before lunch and one after. Yesterday, I began at the usual time. Two hours before lunch I was joined by my good friend Aidan, who paints at the rate of 600 sqft per workday, and who left just as the first coat was finished. I promptly began the second coat, and had lunch at the usual time. One…
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Earlier this week I was rob...er...exploring tombs and I accidently triggered a trap that locked me in a room. With me are a pair of plates, a few thousand tiny statues of gnats and a puzzle that should lead to my escape. I need to place specific numbers of gnats onto each of the two plates. The number of gnats on the left plate needs to be a 3-dig…
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For years you were a lonely prisoner here. But earlier today, you were brought to a courtyard to join the others, where you are all addressed by the Warden. There have been budget cuts, he explains, and the one hundred of you need to leave this facility. Whether you will be sent to another high-security facility, or set free, depends on whether you…
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I have four lengths of rope. I hold them so that you can see all eight ends, but you can’t tell which end connects to which other end. You pick a pair of ends, and I tie them together. We repeat -- you pick, I tie -- until we run out of ends. // What’s the expected value of the number of loops you’ll have at the end? Or, in plain English, if we pla…
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A friend of mine has pictures of his three daughters on his mantle. He took the pictures when each of the girls was a particularly adorable age — the same age for all three of them, as it happens. Unfortunately, this made it impossible for me to determine which was the oldest. So I had to ask him. Since my friend is a puzzle junkie, however, he dec…
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You have just tested positive for a condition known to affect 1% of the population. However, your doctor assures you that the test for this condition is only 90% accurate. You’re not sure whether that’s supposed to make you feel better or not. So, you tell me: assuming no other information, what’s the chance that you have the condition? // Spicines…
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(Errata alert! This episode was re-uploaded with a correction on Monday March 28 at 10am PST. The corrected version is 6m04s long; the old one is 6m02s. Visit http://www.buzzsprout.com/56982 if your feed contains the old version.) // Here's a game you can play with two fair dice, one red and one green. You throw both dice, and use the throw to gene…
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I have two cylindrical glasses that, when full, hold the same amount of water. The short glass has a radius that is half again as large as the tall one’s. Last night, I filled the short one completely, and then I filled the tall one to exactly the same level. // How full was the tall glass? (You can answer as a fraction or a percentage.) // Spicine…
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Welcome to the podcast! Here are the rules, and the first puzzle. // Mr. Patrick teaches math to 15 students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was 80. After he graded Payton's test, the test average became 81. What was Payton's score on the test? // Spiciness: * out …
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