Complicated counting

If two's company, and three's a crowd, then whats four and five ?

Complicated counting




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There is one four-digit whole number n, such that the last four digits of n2 are the original number n

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The first person saw the bridge step on it and crossed,
the second person saw the bridge did not step on it but crossed,
the third person did not see the bridge did not step on it but crossed.
Who are these people?

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John and Jacob are playing bets. John gives $10 to Jacob and Jacob deals four cards out of a normal 52-card deck which are chosen by him completely randomly. Jacob keeps them facing down takes the first card and shows it to John. John has a choice of either keeping it or looking at the second card. When the second card is shown to him, he again has the choice of keeping or looking at the third which is followed by the third card as well; only if he does not want the third card, he will have to keep the fourth card.

If the card that John is choosing is n, Jacob will give it to him. Then the cards will be shuffled and the game will be played repeatedly. Now you might think that it all depends on chance, but John has come up with a strategy that will help him turn the favor in his odds.

Can you deduce the strategy of John?

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There’s a girl who has a large family. She has an equal amount of brothers and sisters, but each brother only has half as many brothers and sisters. What’s the correct amount of brothers and sisters?

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A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

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If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

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Use the numbers 2, 3, 4 and 5 and the symbols + and = to make a true equation. Conditions: Each must be used exactly once and no other numbers or symbols can be used.

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I’m tall when I’m young, and I’m short when I’m old. What am I?

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At a Society election for president, precisely 963 votes were cast.
There is a total of 4 candidates that participate in the election.

The winning candidate exceeds the opponents by 53, 79 and 105 votes.

How many votes do each candidate gets?

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Suppose we lay down two cups in front of you. One of the cups is filled with tea and the other one with coffee. Now we ask you to take a spoonful of tea and mix it with the coffee. At this moment, the coffee cup has a mixture of tea and coffee. You have to take that mixture (spoonful) and add it back to the tea.

Can you now tell if the cup of coffee has more tea or the cup of tea has more coffee?

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There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.