Today’s problem: on a sunny day a greengrocer places 200 lbs of cucumbers in front of his store. At the start of the day they are 99% water. He doesn’t sell any all day but it is a really hot day and by the end of the day the cucumbers are down to 98% water. How many pounds of cucumbers are left in front of the store?
Answer next week
Last week’s puzzle was the Monty Hall problem. It is sufficiently well-known and controversial that it has its own Wikipedia page. The reason it is controversial is that if it is expressed ambiguously then the answer is not clear and erudite professors will write in to complain that you’ve got it wrong. But as I expressed the problem (in the small print), you should definitely switch: you will double your chance of winning to 2/3.
The confusing thing is that intuitively it may seem like after Monty Hall has opened his door that your chances are 50:50 between the two doors. The right way to think of it is that the chance that the car is behind the door you picked starts off was 1/3 and that remains the case after Monty Hall has opened a door. After all, he was always going to open a door with a goat behind it (he’s not opening a random door that happens to have a goat behind it) since he knows where the goats are. So the chance that the car is behind the remaining door must be 2/3. It may help to think of the 100 door version. You pick a door, Monty Hall then opens 98 doors revealing goats, since he knows exactly which 98 doors to open and, except in the unlikely event you’ve actually picked the car, which is the one door he must avoid opening. The door he must avoid opening almost certainly has the car behind it.