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# Monkey & Banana

A ten-meter rope is looped through a pulley attached to the ceiling.Â Half the rope dangles on one side, the other half on the other. At one end of the rope is tied a one-kilo bunch of bananas.At the other end of the rope is a one kilo monkey.If the monkey tries to climb the rope, what will happen?Â

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How many points are there on the globe where, by walking one mile south, one mile east, and one mile north, you reach the place where you started?Â

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# How Many Eggs

A woman was carrying a basket of eggs to market when a passer-by bumped her. She dropped the basket and all the eggs broke. The passer-by, wishing to pay forÂ her loss, asked, 'How many eggs were in your basket? I don't remember exactly, the woman replied, but I do recall that whether I divided the eggs by 2,3,4,5 or 6 there was always one egg left over. When I took the eggs out in groups of seven, I emptied the basket.Â

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4 / 111

# Water Level

If you are on a boat and toss a suitcase overboard, will the water level rise or fall?Â

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# Four Dogs

There are four dogs, each at a corner of a large square.Â Each of the dogs begins chasing the dog clockwise from it. All of the dogs run at the same speed. All continuouslyÂ adjust their direction so that they are always heading straight toward their clockwise neighbor. How long does it take for the dogs to catch each other? Where does thisÂ happen?Â

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There are n persons in a circle, numbered 1 thru n. Going around the circle, every second person is removed from the circle, starting with person number 2, 4, and so on. Show that the number of the last person remaining in the circle can be obtained by writing n in binary, then moving the leftmost 1 to the right. So for example, with n = 13 persons (1101 in binary), the last person is number 11 (1011 in binary).

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We have two white, two red and two blue balls. For each color, one ball is heavy and the other is light. All heavy balls weigh the same. All light balls weigh the same. How many weighings on a beam balance are necessary to identify the three heavy balls?

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A prison has 1000 cells. Initially, all cells are marked with - signs. From days 1 thru 1000, the jailor toggles marks on some of the cells: from + to - and from - to +. On the i

^{th>}day, the signs on cells that are multiples of i get toggled. On the 1001^{th>}day, all cells marked with + signs are opened. Which cells are these?

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# Kirkman's Schoolgirl Problem

Nine schoolgirls are to be arranged in three rows and three columns on four different days so that any pair of schoolgirls is in the same row on exactly one of the four days.Â

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Three wizards are seated in a circular room. A magician shall make hats appear on their heads, one hat per wizard. Hats are either black or white, chosen uniformly at random. A wizard cannot see his own hat. At the sound of a bell, all wizards react simultaneously. A wizard reacts by either announcing a color or keeping quiet. If at least one wizard makes an announcement and if all the announcements are correct, the Wizards have collectively won the game! Wizards are allowed to confer beforehand to devise a strategy. On average, can they win more than half the times the game is played?

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