Podcast
Wes Carroll's Puzzler
Hosted by Wes Carroll · EN
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.)
24episodes
Episodes
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14: O gnats, tango! [**]
Jun 19, 201600:03:31Tap to summarizeEarlier 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-digit palindrome, while the number on the right needs to be a 4-digit palindrome, with a difference between them of 22. I remember that a palindromic number is one where if you read it forwards and backwards, it looks the same. For example, 43534 and 5885 are both palindromes. // Please send in solutions; I want to get out of here. // Spiciness: ** out of ****
Transcribe →13: Order of operands [*]
Jun 5, 201600:08:10Tap to summarizeCindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the problem correctly? // // (Spiciness: * out of ****)
Transcribe →12: One light switch [****]
May 29, 201600:05:48Tap to summarizeFor 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 pass the following test of cleverness and teamwork. // There is a secret room not far from here, and like your individual cells, it is soundproof, lightproof, and in all other ways impervious to communication. The only object in this room is a single light switch, not connected to anything. It is currently in the off position. // In an hour, you will each be sent back to your cells. One of you will be selected at random to visit the room. While there, that prisoner may choose to flip the switch or not. No other actions will be permitted. Then another prisoner will be chosen at random. And again and again and again, over and over, always at random. // At any point, any of you may declare that all of you have visited the room. If the declaration is true, you will all go free. If not, then you will never again see the light of day. // You have one hour to formulate your strategy. // How will you arrange for everyone to go free? // Note: you have no idea how often prisoners will be sent to the room. Any solution whereby you try to “run out the clock” will be considered incorrect. A correct solution is one for which a declaration proves that all prisoners have visited the room at least once each. // Oh, one last thing: if it’s still not enough of a challenge for you, try solving the variant in which the switch starts in a random position. // (Spiciness: **** out of ****)
Transcribe →11: The loopiest puzzler [***]
May 22, 201600:03:00Tap to summarizeI 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 play this game a zillion times, what’s the average number of loops I’ll get per game? Note: the correct answer is not a whole number.
Transcribe →10: Eight's too many [**]
May 15, 201600:06:14Tap to summarizeIn the eight-term sequence "a, b, c, d, e, f, g, h", c represents 5, and the sum of any three consecutive terms is 30. What’s a+h? (Spiciness: ** out of ****)
Transcribe →09: Coin flip winner [***]
May 8, 201600:06:34Tap to summarizeWe’re going to play a simple coin-flip game. We take turns flipping a fair coin. The first one to get “heads” wins. You go first. // What’s your chance of winning? // Spiciness: *** out of ****
Transcribe →08: Strawberry ice cream [***]
May 1, 201600:03:21Tap to summarizeA 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 declined to answer directly, telling me only that the product of their current ages was 72. “However,” he added, “since that isn’t enough information to determine their ages, I’ll also tell you that the sum of their ages happens also to be the number of our street address.” (Of course, I understood that each daughter’s age was to be considered a whole number for purposes of this puzzle.) I darted outside to check the number on his mailbox. I was daunted to discover that I still didn’t have enough information to determine their ages, and I returned to tell him so. “That is an astute observation,” he said, smiling. “So you’ll be glad to know that my oldest daughter prefers strawberry ice cream.” Finally! I knew their ages. Do you? // Spiciness: *** out of ****
Transcribe →07: Kiana's twin brothers [*]
Apr 24, 201600:03:17Tap to summarizeKiana has two older twin brothers. The product of their three ages is 128. What is the sum of their three ages? // Spiciness: * out of **** // (Today’s puzzler comes from the 2009 AMC 10 exam. Learn more at dtmath.com/amc.)
Transcribe →06: That sounds accurate [***]
Apr 17, 201600:02:35Tap to summarizeYou 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? // Spiciness: *** out of ****
Transcribe →05: Ted's three statements [**]
Apr 10, 201600:02:04Tap to summarizeTed has three numbered statement for us to consider, and he wants to know whether the third one is true. Here they are: // 1. There are three numbered statements. 2. Two of the three statements are false. 3. You know the answer to the question. // So: is Statement 3 true? // Spiciness: ** out of ****
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