Here are several puzzles. I was going to put more here, but... hopefully I'll have time to add more later.
Twelve Gold Coins
You have in front of you 12 gold coins; one is known to be fake, and the fake coin is either slightly heavier or lighter than the other coins. given a simple balance, and given that you are only allowed to use the balance three times, find a method by which you can determine which coin is the fake coin, and whether it is heavier or lighter than the others, for all possible outcomes.
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O O O O O O O O O O O O
Twelve Bags of Gold Coins
In front of you are twelve bags full of gold coins, of which one bag is filled with fake gold coins. Real gold coins weigh 12 grams each, while fake coins weigh 11 grams each. Using a balance that displays mass to the gram, how many weighings are required to determine which bag contains the fake coins?
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01234567890123456789012345678901234567890123456789012345678901234567890
The Eight Queens Problem
The object this time is to place eight queens from the game of chess and to place them on a chess board such that no queen can capture any other queen--i.e., one queen on each row & column, and no more than one queen on any given diagonal line on the 8x8 board...
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. Q . . . . . .
. . . Q . . . .
. . . . . Q . .
? ? ? Q . . . . . . . Q ??
. . . . . . . .
. . . . Q . . .
. . Q . . . . .
. . . . . . . Q
Almost, but not quite...
Three hats
Three (intelligent) people are put in a room, each wearing a hat. The hats are identical in all aspects but their color--either red or white. No one can see his/her own hat's color. The three are desparate to get out of the room, but are told that the only way out is to figure out what color hat they are wearing; no discussions, verbal or otherwise, are allowed amongst the three. They each have only one chance to guess their hat color, and must also explain why they think so. They are given only one hint; that at least one hat is white.
After several minutes of silence, one of the three suddenly answers, and explains the reason, correctly. What was the answer, and the logical reason behind it?
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red red red? red red white?
red white white? white white white?
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One plus One
Something is wrong with the seemingly logical procedure below; can you see where?
First, let a = b
Multiplying a to each side: a2 = ab
Subtracting b2 from both sides: a2 - b2 = ab - b2
Factor both sides: (a + b)(a - b) = b(a - b)
Then divide both sides by (a - b): a + b = b
From the original assumption, a = b, so a + a = a
Finally, divide both sides by a: 1 + 1 = 1
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1+1=1+1=1+1=1+1=1+1=1+1=1+1=1+1=1+1=1+1=1+1=1+1=1+1=1+1=1+1=1+1=1+1=1 ???
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