Puzzles
Puzzles of logic and imagination
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Puzzles Puzzles of logic and imagination |
A woman wins a quiz show and it's prize time.
There are three closed doors. Behind each of two of the doors, the quizmaster tells her, is a smelly, putrid goat. Behind the other, lies a mega-turbo sportscar. She gets whatever is behind the door she picks.
So, she picks a door. The quizmaster - who knows what is behind each door - then opens one of the other two doors to reveal a goat.
"You can now stick to the door you've already picked, or you can switch to the remaining closed door", says the quizmaster.
If she wants to maximise her chances of winning the sportscar, should she stick or switch, or does it not make any difference?
A school has 100 pupils, numbered 1-100 (it's an English public school so names aren't necessary). Each pupil has a locker.
Initially, all the lockers are closed.
Pupil 1 switches the state of all the lockers ("switches the state" means that she opens a locker if it is closed, and closes it if it is open - since they are all initially closed, this means that she opens all the lockers).
Pupil 2 then switches the state of all lockers numbered 2, 4, 6, ... 100 (ie multiples of 2) (since they've all just been opened by Pupil 1, this means that she closes lockers 2, 4, 6, ... 100).
Pupil 3 then switches the state of all lockers numbered 3, 6, 9, ... 99 (ie multiples of 3) (ie she closes a locker if it's open, and opens it if it's closed).
This continues until Pupil 100 switches the state of (ie opens or closes) locker 100.
How many lockers are now open?
A train is 100 miles from the station, travelling towards it at 100 mph. A titanium bee starts at the train's buffers and flies at 200 mph towards the station. When it reaches the buffers at the station, it instantaneously turns 180o and carries on flying at 200 mph back towards the train. When it reaches the train's buffers it again turns 180o and flies towards the station. It continues to do this until it is crushed between the train and the station buffers as the train crashes into the buffers.
How far does the bee fly before it is crushed?
Two players sit at a round table. Each player has a large pile of the various denominations of euro coins. The players take turns to put a coin on the table. The coins must not overlap ie they must lie flat on the table (they can overhang the edge as long as they don't fall off).
The winner is the player who puts the last coin down.
If you are playing and are offered the choice of going first or second, which should you choose and what would your strategy be?
A chessboard is missing two squares from opposite corners. There are 31 dominoes, each of which covers exactly two squares on the chessboard.
Is it possible to cover the chessboard with the 31 dominoes?
A London man has two girlfriends. One lives in North Acton and the other in Mile End. He works near Holborn.
To avoid taking any responsibility for his actions, after work he arrives randomly at the Central Line in Holborn tube station and takes whichever train comes first. If it's going West then he sees the North Acton girl, if it's going East he sees the Mile End girl.
The trains run every 10 minutes in each direction.
The funny thing is, even though he arrives randomly, he sees the North Acton girl nine times as often as the Mile End girl.
How can this be so?
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There are two ropes around the equator - the first is at ground level, and the second is a foot above the first.
So, the second rope creates a larger circle than the first.
By approximately how much is the second rope longer than the first?
A) 6 feet
B) 6 miles
C) 600 miles
There is a monastery at the top of a mountain, with a single trail leading to it. A monk is at the foot of the trail at the bottom of the mountain. He sets off at 06:00 and slowly makes his way up, stopping from time to time to admire the view and take victuals. He eventually arrives at the monastery at 18:00 (6pm).
He stays the night, and leaves the next morning at 06:00. Again, he goes slowly downhill, smelling the flowers as he goes. He arrives at the foot of the trail at 18:00 (6pm).
Is there any spot on the path where the monk finds himself at exactly the same time on each of the two days?
U2 are due to start their concert in 17 minutes. It's night, they have one torch (US: flashlight) between them, and they have to cross a rickety bridge that can handle only two people at a time. So, they need to cross the bridge either in pairs (since they need the flashlight to see) at the speed of the slower person, or individually, and always with the torch. (Someone needs to carry the torch back as throwing it would be too risky).
Due to their various stages of physical degradation, each of the four band members takes 1, 2, 5 and 10 minutes to cross the bridge.
How can they all get across the bridge in the 17 minutes?
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© 2002 Ian Hadden |