Clever Puzzles

Three Palefaces were taken captive by a hostile Indian tribe. According to tribe’s custom they had to pass an intelligence test, or die.
The chieftain showed 5 headbands – 2 red and 3 white. The 3 men were blindfolded and positioned one after another, face to back. The chief put a headband on each of their heads, hid two remaining headbands, and removed their blindfolds. So the third man could see the headbands on the two men in front of him, the second man could see the headband on the first, and the first could not see any headbands at all.
According to the rules any one of the three men could speak first and try to guess his headband color. And if he guessed correctly – they passed the test and could go free, if not – they failed. It so happened that all 3 Palefaces were prominent logicians from a nearby academy. So after a few moments of silence, the first man in the line said: “My headband is …”.
What color was his head band? Why?View SolutionSubmit Solution 949.4K views
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Three cannibals and three anthropologists have to cross a river.
The boat they have is only big enough for two people. The cannibals will do as requested, even if they are on the other side of the river, with one exception. If at any point in time there are more cannibals on one side of the river than anthropologists, the cannibals will eat them.
What plan can the anthropologists use for crossing the river so they don’t get eaten?
Note: One anthropologist can not control two cannibals on land, nor can one anthropologist on land control two cannibals on the boat if they are all on the same side of the river. This means an anthropologist will not survive being rowed across the river by a cannibal if there is one cannibal on the other side.
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There are three boxes. One is labeled “APPLES” another is labeled “ORANGES”. The last one is labeled “APPLES AND ORANGES”. You know that each is labeled incorrectly. You may ask me to pick one fruit from one box which you choose.
How can you label the boxes correctly?
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Three men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognizes the three as friends and asks the waiter to return $5 to the men.
The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.
Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14…..where has the other $1 gone from the original $15?
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There is an equilateral triangle and three bugs are sitting on the three corners of the triangle. Each of the bugs picks up a random direction and starts walking along the edge of the equilateral triangle. What is the probability that none of the bugs crash into each other?
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A king wants an advisor and comes to ask the 3 wisest sages.
He blindfolds them and put the hats on their head. Afterwards, the king takes off their blindfolds. He tells them that their hat is either blue or white. He tells them that whoever can deduce the color of their hat will be his next advisor. Also he tells them that at least one of the sages will be wearing a blue hat. The sages can all see each other’s hats except of course, their own. Sage A sees that the other 2 are wearing blue hats.
For hours no one spoke, then Sage A stands up and tells theĀ king the colour of his hat. What color is it and how does he know?View SolutionSubmit Solution 952.2K views
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