Riddle #1076

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logicshort

Clever thief sentenced to death

In olden days you are a clever thief charged with treason against the king and sentenced to death. But the king decides to be a little lenient and lets you choose your own way to die. What way should you choose? Remember, your're clever!
I would have chosen to die of "old age". Did you?
91.27 %
66 votes

logicmath

New York Hair

You are visiting NYC when a man approaches you. "Not counting bald people, I bet a hundred bucks that there are two people living in New York City with the same number of hairs on their heads," he tells you. "I'll take that bet!" you say. You talk to the man for a minute, after which you realize you have lost the bet. What did the man say to prove his case?
This is a classic example of the pigeonhole principle. The argument goes as follows: assume that every non-bald person in New York City has a different number of hairs on their head. Since there are about 9 million people living in NYC, let's say 8 million of them aren't bald. So 8 million people need to have different numbers of hairs on their head. But on average, people only have about 100,000 hairs. So even if there was someone with 1 hair, someone with 2 hairs, someone with 3 hairs, and so on, all the way up to someone with 100,000 hairs, there are still 7,900,000 other people who all need different numbers of hairs on their heads, and furthermore, who all need MORE than 100,000 hairs on their head. You can see that additionally, at least one person would need to have at least 8,000,000 hairs on their head, because there's no way to have 8,000,000 people all have different numbers of hairs between 1 and 7,999,999. But someone having 8,000,000 is an essential impossibility (as is even having 1,000,000 hairs), So there's no way this situation could be the case, where everyone has a different number of hairs. Which means that at least two people have the same number of hairs.
91.22 %
48 votes

cleanshortwhat am I

Shut up in a wooden case

I am taken from a mine, and shut up in a wooden case from which I’m never released, and yet I am used by many. What am I?
Pencil lead.
90.67 %
45 votes

logicmath

In a bank

A women walks into a bank to cash out her check. By mistake the bank teller gives her rupee amount in change, and her paise amount in rupees. On the way home she spends 5 paise, and then suddenly she notices that she has twice the amount of her check. How much was her check amount ?
The check was for Rupees 31.63. The bank teller gave her Rupees 63.31 She spent .05, and then she had Rupees 63.26, which is twice the check. Let x be the rupees of the check, and y be the paise. The check was for 100x + y paise He was given 100y + x paise Also 100y + x - 5 = 2(100x + y) Expanding this out and rearranging, we find: 98y = 199x + 5 or 199x ≡ -5 (mod 98) or 98*2*x + 3x ≡ -5 (mod 98) 3x ≡ -5 ≡ 93 (mod 98) this quickly leads to x = 31
90.47 %
44 votes

logicmath

A grandfather's clock

A grandfather's clock chimes the appropriate number of times to indicate the hour, as well as chiming once at each quarter hour. If you were in another room and hear the clock chime just once, what would be the longest period of time you would have to wait in order to be certain of the correct time?
You would have to wait 90 minutes between 12:15 and 1:45. Once you had heard seven single chimes, you would know that the next chime would be two chimes for 2 o'clock.
90.47 %
44 votes