A mother has twelve children, each born in a different month. They want to go to the beach. She says she’ll take them if they can win a game. She puts the name of each child on a card and tells them she will place the cards face-down in a row on a table in the next room.
She’ll randomly call one child in. The child can turn over cards one at a time, up to half the cards, looking for his or her own name.
If that child finds his or her own name, he or she will be sent outside to play, and won’t be able to communicate with the children still waiting to take a turn. The mother will turn all the cards back face-down, keeping them in the same order, and will randomly call in another child and repeat the process. In order for the children to win the game and go to the beach, all the children must be successful in finding their own names. If any child fails, the game is over, and there will be no trip to the beach! The children can consult each other before their mother starts the game, but those who have already taken a turn cannot contact the others or leave any clues for them.
The children talk among themselves and devise a strategy that all the children will be able to follow perfectly. The game begins, and the first child is called into the room where the game is taking place. A few minutes later, he comes back into the room with the other children, grinning widely. “Pack your swimsuits and your towels!” he says. “We’re going to the beach!”
The child is correct, and knows for certain that the inevitable outcome of the game is that the children will win. How many cards did he turn over before he found his name?
puzzle by Harvey Lerman
permutations n Combinations
Lauren Johnson says
This just plagiarizes the 100 prisoners problem.
Harvey Lerman says
Yes it does. But tries to hide that by removing numbers from the problem (except for one hint giving 12 months-though I had originally had “every month of the year but each in a different month”) and looks like a friendly family instead of 100 prisoners. Even you didn’t notice that until I gave the solution. (But no proof…)
Chandra Sekhar says
cards are placed in the order of months from January to December. So a child born on a particular month can easily pick up his card, He or She has to pickup maximum of 2 Cards only (One Card to identify from which side month starts and the second for his birth month)
He turns over zero of the cards because the game has not been yet started, the child is only being optimistic that they’ll surely win.
HIMA V TOM says
Only 1, all the names are written on the same card.
Ramya Viy says
Only 1 ???
Lakshya Jain says
sumeet Vazirani says
i think that child must have turned all cards !!!!!
Aravind Kumar says
Harvey Lerman says
The Child turns over the card corresponding to his birth month and finds someone else’s name. He then turns over the card corresponding to that child’s month and finds another name. He continued like this until he found his own name under the 6th card he turned. By not finding his name until half the cards had been turned, He knew that all the kids after him would find their own names by the time they turned over 6 cards, so they would win! The proof for this requires knowledge of statistics/probability that can not be provided in this short answer.
So the answer to this puzzle is “He found his own name on the 6th card he turned over.”