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.)

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 r…

23: Your prime choice [***]

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

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 mist…

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 c…

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

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. …

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…

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 h…

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….

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 …

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 numbe…

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…

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 facil…

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. // W…

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 ****)

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

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 determ…

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.)

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, y…

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: // 1. There are three numbered statements. 2. Two of the three statements are false. 3. You know the answer to the question. …

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? // Bonus points if you also tell me the number of distinct ways you can arrange them in a circle instead of a line. //…

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 y…

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…

01: Peyton’s great score [*]

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…