Friday puzzle: Monty Hall

Last week’s puzzle was the camel and the bananas. Firstly, a moment’s thought shows that the camel can’t get any bananas to market in one go. It is 1000 km away and so the camel will eat all of its maximum load of 1000 bananas and then be stuck at the market anyway. The least number of loads the camel needs to take from the plantation is 3 (3000 bananas, maximum load of 1000). So the camel will have to make 3 trips from the plantation to some intermediate point to move all 3000 bananas (less the ones eaten), meaning 5 trips in all across that distance (3 outgoing, 2 returning). If we arrange that after those 5 trips precisely 2000 bananas are left then it can make two trips from that intermediate point to a second intermediate point, meaning 3 trips across that distance (2 outgoing, 1 returning). At this point we want there to be precisely 1000 bananas left with which the camel sets off to the market. The first point needs to be 200 kilometers away (so that 1000 bananas are consumed on the 5 trips leaving 2000). The second point needs to be 333 1/3 miles further on (533 1/3 kilometers from the plantation) so that 1000 bananas are consumed on those 3 trips.

So it plays out like this. The camel takes 1000 bananas to the first intermediate point 200 kilometers away. There it drops 600 bananas and returns with 200 (and it already ate 200). Again it takes 1000 bananas, drops 600 and returns with 200. Then it takes the last 1000 bananas, gets to the intermediate point, picks up another 200 (to replace the 200 it already ate) and takes them to the second intermediate point a further 333 1/3 kilometers away. There it drops 333 1/3 bananas and returns with 333 1/3 bananas. Then it takes a the remaining 1000 bananas from the first intermediate point to the second intermediate point, arriving with 666 2/3 bananas. It picks up the 333 1/3 bananas already at the second intermediate point (making 1000) and sets off for market 466 2/3 kilimeters away where it arrives with 533 1/3 bananas out of the original 3000.

Today’s puzzle: You are on Let’s Make a Deal. There are three doors. Behind one door is a car. Behind the other two doors are goats. You pick door number 1. Monty Hall, the host, who knows what is behind each door, then opens a different door to show you a goat. He offers you the choice of sticking with your choice of door number 1 or switching to the remaining closed door. Should you switch?

To make the problem unambiguous, assume that after you pick a door, Monty Hall must then open a door and he must pick a door that he knows has a goat behind it and that he must then give you the chance to switch.

This entry was posted in puzzles. Bookmark the permalink.

Comments are closed.