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Monty Hall variant (Posted on 2018-09-30) Difficulty: 3 of 5
There are three closed doors. One has a new car, one has the keys to the car and one has a goat. These prizes are randomly assigned.

There are two players: the first player has to find the car, the second player has to find the keys to the car. If both players succeed they win the car.

The first player enters the room and may open any two of the three doors, one after the other. If successful, the doors are closed again and the second player enters the room. The second player may also open two of the three doors, but cannot communicate with the first player.

Surprisingly there is a strategy where the probability of winning is better than (2/3)2. Find it.

No Solution Yet Submitted by Jer    
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Monty Hall | Comment 2 of 6 |
As was mentioned while this puzzle was in the queue, Monty Hall died one year ago today. I first remember Monty Hall from his Bingo at Home TV show in the 1950's.  I see this was on channel 5 in New York, which was the local affiliate of the DuMont network, which apparently became defunct just as Bingo was starting up, so channel 5 was then independent (it's now a Fox affiliate).

I remember that his favorite letter-number to call was O-0 (oh-oh), but couldn't figure how this was possible as there's no zero on standard cards, and certainly not under the O. But since people were playing at home, for prizes, there was an unusual way people got their cards. The home player filled the top row with the last five digits of his phone number, or any phone number in the same column as his in the phone directory (remember those?). Each column was then completed by placing in each position the number one higher than the one above it, mod 10. So there were 50 possibilities to call: each combination of letter of BINGO with a digit from zero to 9.

An entire eposode is at


including early-on an occurrence of O-0, and an explanation of how to fill in you at-home card(s). All the winners announced were in the New York metro area, so apparently this was indeed a local show, given the at-the-time recent demise of the DuMont network.

  Posted by Charlie on 2018-09-30 10:04:33
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