Wes Carroll's Puzzler

Wes Carroll

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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.)

Available episodes

Newest first

Oldest first

Dec 25, 2016

24: Santa's big sleigh [****]

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: **** out of ****

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Nov 6, 2016

23: Your prime choice [***]

What’s the largest 2-digit prime factor of “200 choose 100”?
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Spiciness: *** out of ****

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Oct 2, 2016

22: Split the check [*]

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 of each pair of people.
//
Spiciness: * out of ****

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Sep 4, 2016

21: The faulty odometer [***]

A faulty car odometer proceeds from digit 3 to digit 5, always skipping the digit
4, regardless of position. For example, after traveling one mile the odometer
changed from 000039 to 000050. If the odometer now reads 001729, how many
miles has the car actually traveled?
//
Spiciness: *** out of ****

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Aug 28, 2016

20: The middle digit [**]

How many three-digit numbers satisfy the property that the middle digit is the average of the first and the last digits?
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Spiciness: ** out of ****

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Aug 14, 2016

19: The token tax [**]

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 be in the game?
//
Spiciness: ** out of ****

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Jul 31, 2016

18: The circular track [***]

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 listeners.)
//
Spiciness: *** out of ****

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Jul 24, 2016

17: The red one [***]

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 the dogwood rose, but the cherry and the dogwood rose were not adjacent. I told her that she hadn’t given me enough information, so she just laughed and told me that she could tell me the color of the first one or the color of the last one, but it wouldn’t help if she did either one.
//
What color was the second house?
//
Spiciness: *** out of ****
//
Note: Not having paper makes this one especially difficult. If you give yourself paper, I think you can rate this puzzle as two chili peppers of spiciness instead of three.

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Jul 17, 2016

16: In 80 days [*]

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 to get within a few minutes of her house, but couldn’t give her an exact location.
//
Where does she live?
//
Spiciness: * out of ****

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Jul 3, 2016

15: Coats of paint [***]

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 hour before quitting time, I had painted a second coat everywhere except where Aidan had painted that morning. If we each have the same workday, and if each of us works at a constant rate (albeit not necessarily the same rate as the other), what was the area of the wall?
//
Spiciness: *** out of ****

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Jun 19, 2016

14: O gnats, tango! [**]

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-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 ****

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Jun 5, 2016

13: Order of operands [*]

Cindy 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 ****)

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May 29, 2016

12: One light switch [****]

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 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, alw…

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May 22, 2016

11: The loopiest puzzler [***]

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 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.

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May 15, 2016

10: Eight's too many [**]

In 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 ****)

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May 8, 2016

09: Coin flip winner [***]

We’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.
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What’s your chance of winning?
//
Spiciness: *** out of ****

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May 1, 2016

08: Strawberry ice cream [***]

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 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…

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Apr 24, 2016

07: Kiana's twin brothers [*]

Kiana 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.)

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Apr 17, 2016

06: That sounds accurate [***]

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?
//
Spiciness: *** out of ****

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Apr 10, 2016

05: Ted's three statements [**]

Ted has three numbered statement for us to consider, and he wants to know whether the third one is true. Here they are:
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1. There are three numbered statements.
2. Two of the three statements are false.
3. You know the answer to the question.
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So: is Statement 3 true?
//
Spiciness: ** out of ****

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Apr 3, 2016

04: Many stuffie lines [*]

You have four stuffed animals. You line up three of them at a time, always single file. How many distinct lineups are possible?
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Bonus points if you also tell me the number of distinct ways you can arrange them in a circle instead of a line.
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Spiciness: * out of ****

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Mar 28, 2016

03: Two square dice [***]

(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 generate an infinitely long sequence of numbers, like this: first, you write down the red number. Then you add in the green number, write down the result, add the green again, write down that result, and so on.
//
You decide to play the game once today. What’s the chance that the sequence made by your dice throw will contain a perfect square?
//
Spiciness: *** out of ****

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Mar 21, 2016

02: Glass half full? [*]

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.
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How full was the tall glass? (You can answer as a fraction or a percentage.)
//
Spiciness: * out of ****

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Mar 14, 2016

01: Peyton's great score [*]

Welcome to the podcast! Here are the rules, and the first puzzle.
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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 of ****

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