Long Puzzles
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You decide to play a game with your friend where your friend places a coin under one of three cups. Your friend would then switch the positions of two of the cups several times so that the coin under one of the cups moves with the cup it is under. You would then select the cup that you think the coin is under. If you won, you would receive the coin, but if you lost, you would have to pay.
As the game starts, you realize that you are really tired, and you don’t focus very well on the moving of the cups. When your friend stops moving the cups and asks you where the coin is, you only remember a few things:
He put the coin in the rightmost cup at the start.
He switched two of the cups 3 times.
The first time he switched two of the cups, the rightmost one was switched with another.
The second time he switched two of the cups, the rightmost one was not touched.
The third and last time he switched two of the cups, the rightmost one was switched with another.
You don’t want to end up paying your friend, so, using your head, you try to work out which cup is most likely to hold the coin, using the information you remember.
Which cup is most likely to hold the coin?
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Sonia is going on an extended trip for three weeks. She lives in a remote area where there are frequent electrical power outages which can last up to three or four days. Sonia has quite a bit of food in her freezer which would go bad if it thawed and then re-froze. She does have digital clock and a VCR which would flash 12:00 if the power went out.
Unfortunately the clock and VCR flash even if the power only goes out for a few seconds.
What can Sonia do so that when she returns home she will be able to determine whether the power was out long enough to thaw her food?
Asking a neighbour whether the power was out, isn’t a reliable option because the nearest house is half a mile away, and one house may have power, while another house may have no power. She won’t be able to have a neighbour check on her house every day, and has no one to house sit.
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You are on your way to visit your Friend, who lives at the end of the hill. It is his birthday, and you want to give him the cakes you have made. Between your house and his house, you have to cross 5 bridge, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.
How many cakes do you have to leave home to make sure that you arrive at friend house with exactly two cakes?
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