• I try to solve at least one maths puzzle everyday. Here are a few that I have found interesting and fun:

  1. Your boss tells you to bring him a cup of coffee from the company vending machine. The problem is the machine is broken. When you press the button for a drink, it will randomly fill a percentage of the cup (between 0 and 100 percent). You know you need to bring a full cup back to your boss. What’s the expected number of times you will have to fill the cup? (source: cseblog.com)

  2. In an election, two candidates, Albert and Benjamin, have in a ballot box a and b votes respectively, a>b, for example, 3 and 2. If the ballots are randomly drawn and tallied, what’s the chance that at least once after the first tally the candidates have the same number of tallies?

  3. You have 25 horses, you want to pick the fastest 3 horses out of those 25. In each race, only 5 horses can run at the same time. What is the minimum number of races required to find the 3 fastest horses without using a stopwatch? (source: a friend asked me)

  4. Pick independent random numbers at uniform from [0,1] and add them together. How many random numbers do you expect to need before the total first exceeds 1? (Source: Twitter @octonion) (I loved this!)

  5. How thick should a coin be to have a 1/3 chance of landing on edge? (Was trying to make coin stand on the magnetic strip of my laptop and started thinking of this. Von Neumann was asked this and he answered it in 20 seconds)

  6. A hen wants to cross a one-way road at a point, where cars drive by according to a homogeneous Poisson process with rate λ per unit time. It takes c time units for the hen to cross the road. Assume that the hen starts to cross the road immediately when there is a chance to do it without being run over. Let T denote the total waiting time for the hen till the instant it starts crossing; write an expression for T and compute the expected total waiting time. (Source: Facebook - miss such FB feeds)

  7. Let’s say we have to build a cube of shape N x N x N (in some units) by stacking smaller cubes each of size 1 x 1 x 1 (in some units). Each of the smaller cubes (unit cubes) come in one of the K distinct colors and we have sufficient supply of cubes of each color. How many distinct ways are there in which we can stack these cubes to form the bigger cube? [Bigger cubes which can be rotated or mirrored to each other are not considered distinct.] (Source: Came up with this while solving a problem in my submitted paper)

  8. Consider a standard chessboard with 64 squares. The Devil is in the room with you. He places one coin on each of the 64 squares, randomly facing heads or tails up. He arbitrarily selects a square on the board, which he calls the Magic Square. Then you have to flip a coin of your choosing, from heads to tails or vice versa. Now, a friend of yours enters the room. Just by looking at the coins, he must tell the Devil the location of the Magic Square. You may discuss any strategy/algorithm with your friend beforehand. What strategy do you use to do this? (Source: Somewhere on Reddit)

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