Podcast – 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 ****

Podcast – 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 ****

Podcast – 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 ****

Podcast – 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, 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 ****)

Podcast – 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.