Rivercrossing and Runaway Math Puzzles



A river. Three cannibals and three missionaries are standing on one bank. There is a boat with maximum capacity of two people. How do they get to the other side so that missionaries are never outnumbered by cannibals on any bank?

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Group of friends is trapped in a burning house. The house is going to collapse in 12 minutes so they desperately want to get out. They have to run through a hallway which is in flames. If someone wants to pass through he has to have a fire extinguisher to hold the flames back at least a little. Problem is that the friends have only one.

Only two people can go at once. Than somebody has to return with the extinguisher and other two can go.

There is one fireman among the friends who moves through flames with ease and he can ran through the hallway in one minute. His best friend who is in great shape can run through in 2 minutes. There is an older man who needs four minutes and a drunken guy who will need 5 minutes to pass through. If two people go together they move at speed of the slower one.

How will they do it so that they all get out before the house collapses?

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Prison guards are bored so during dinner they announce the prisoners that they will play a game:

In the morning they will stand in a line so that every prisoner will see all standing in front of him but no one behind him. Guards will randomly paint red or white stripe on their back.

They will ask prisoners one by one from the last to the first. They will be allowed to say just one word “red” or “white”. If the prisoner says the color he has on his back he may go home in opposite case he will be executed without delay.

The prisoners are in one cell during the night and they can discuss the tactics.

Which is the best? How many will survive?

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Goat and Wolf

A river. Shepherd wolf goat and a cabbage on one bank. Wolf wants to eat the goat wants the cabbage. Into the shepherd can take only one animal or a cabbage in the boat. Two animals or an animal and a cabbage can't fit in the boat together with the shepherd. Surprisingly neither wolf nor goat can paddle.

How does the shepherd get wolf goat and cabbage to the other side so that goat never stays with wolf or cabbage without shepherds' supervision?

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