Maths fun

Public thinks mathematics is a static discipline. Asking a mathematician what’s new is like asking an engineer what’s new with the wheel.

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fun 1:

There are three cards..

one which has two crosses on both sides
one which has two circles on both sides
one which has a circle on one side and a cross on the other
If I randomly select one card and I see that there is a cross on one side of that card, what is the probability there is a cross on the other side too?

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fun 2:

One half men eat one half hot dogs in one half seconds. How long does it take 6 men to eat 6 hot dogs?

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fun 3:

A certain mathematician, his wife, and their teenage son all play a fair game of chess. One day when the son asked his father for 10 dollars for a Saturday night date, his father puffed his pipe for a moment and replied, "Let's do it this way. Today is Wednesday. You will play a game of chess tonight, tomorrow, and a third on Friday. If you win two games in a row, you get the money."
"Whom do I play first, you or mom?"
"You may have your choice," said the mathematician, his eyes twinkling.
The son knew that his father played a stronger game than his mother. To maximize his chance of winning two games in succession, should he play father-mother-father or mother-father-mother?

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“There are 3 types of people in the world. People who can count, and people who can't!”~ Pythagoras on Mathematics“ ... There are 10 types of people in the world. Those who understand binary, and those who can't!”~ HAL on Mathematics ... “This isn't purgatory! This is HELL!!!”~ Everybody on Mathematics .... “It's not really science. It's more of a religion. You have to believe 2 and 2 suddenly becomes 4.”~ Bill Gates on Mathematics

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fun 4:

The blue armies want to synchronize their attacks. However, their only communication medium is to send messengers on foot down into the valley, where they might be captured and the message lost. Question is: Does a protocol exist that allows the blue armies to win? (Is there way to make sure that both blue armies attack in unison? ) If so, what is it?

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fun 5:

Imagine that a white army is encamped in a valley. On both of the surrounding hillsides are blue armies. The white army is larger than either of the blue armies alone, but together the blue armies are larger than the white army. If either blue army attacks by itself, it will be defeated, but if the two blue armies attack simultaneously, they will be victorious.

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