We should probably start with the solution to last week’s puzzle:
Separate the chips into two piles any way you like, one with 23 chips in it, and the other with 994. You can’t see how many are facing white or black up, but it doesn’t matter. Flip all of the chips in
the pile with 23 chips. Suppose n of the 23 were originally black before you flipped them, so 23-n of them are black in the pile of 994 chips. After you flip them 23-n of them are black in the pile of 23 chips!
And now for something a little different. I learned this from Martin Gardener many years ago, and it is one of those rare puzzles which has an immediate real-life application, at least for mathematicians of my generation. We tend to drink a lot of coffee!
Suppose that you are waiting for a train and decide to buy a coffee to drink on the journey. The train is unreliable so you are not exactly sure when it will arrive, but you don’t want to risk missing the train OR the coffee by leaving it too late to join the queue, so you go ahead and buy the coffee. You like your coffee with milk, so they give you a small pot of milk with the coffee. But you also like it hot. Should you put the milk in straight away, wait to add the milk on the train, or doesn’t it matter?