Many years ago a wealthy old man was near death. He wished to leave his fortune to one of his three children. The old man wanted to know that his fortune would be in wise hands. He stipulated that his estate would be left to the child who would sing him half as many songs as days that he had left to live.The eldest son said he couldn't comply because he didn't know how many days his father had left to live and besides he was too busy. The youngest son said the same thing. The man ended up leaving his money to his third child a daughter. What did his daughter do?
Every other day, the daughter sang her father a song.
See also best riddles or new riddles.logicmathshort
Is half of two plus two equal to two or three?
Three. It seems that it could almost be either, but if you follow the mathematical orders of operation, division is performed before addition. So... half of two is one. Then add two, and the answer is three.logicmath
There are n coins in a line. (Assume n is even). Two players take turns to take a coin from one of the ends of the line until there are no more coins left. The player with the larger amount of money wins.
Would you rather go first or second? Does it matter?
Assume that you go first, describe an algorithm to compute the maximum amount of money you can win.
Note that the strategy to pick maximum of two corners may not work. In the following example, first player looses the game when he/she uses strategy to pick maximum of two corners.
Example 18 20 15 30 10 14
First Player picks 18, now row of coins is
20 15 30 10 14
Second player picks 20, now row of coins is
15 30 10 14
First Player picks 15, now row of coins is
30 10 14
Second player picks 30, now row of coins is
First Player picks 14, now row of coins is
Second player picks 10, game over.
The total value collected by second player is more (20 + 30 + 10) compared to first player (18 + 15 + 14). So the second player wins.
Going first will guarantee that you will not lose. By following the strategy below, you will always win the game (or get a possible tie).
(1) Count the sum of all coins that are odd-numbered. (Call this X)
(2) Count the sum of all coins that are even-numbered. (Call this Y)
(3) If X > Y, take the left-most coin first. Choose all odd-numbered coins in subsequent moves.
(4) If X < Y, take the right-most coin first. Choose all even-numbered coins in subsequent moves.
(5) If X == Y, you will guarantee to get a tie if you stick with taking only even-numbered/odd-numbered coins.
You might be wondering how you can always choose odd-numbered/even-numbered coins. Let me illustrate this using an example where you have 6 coins:
18 20 15 30 10 14
Sum of odd coins = 18 + 15 + 10 = 43
Sum of even coins = 20 + 30 + 14 = 64.
Since the sum of even coins is more, the first player decides to collect all even coins. He first picks 14, now the other player can only pick a coin (10 or 18). Whichever is picked the other player, the first player again gets an opportunity to pick an even coin and block all even coins.logicmathshort
There is a box full of marbles,
all but two are blue,
all but two are green,
and all but two are red.
How many marbles are in the box ?
There are 3 marbles (1 blue, 1 green, and 1 red).logic
A number of people have broken the sound barrier, either in a super-fast car, or in nice fancy planes. However, hundreds of years ago it was broken on horseback. How?
Many people who ride horses carry whips. They crack the whip while they ride the horse. When a whip is cracked, the tip travels faster than the speed of sound, which makes the loud snap. It actually creates a miniature sonic boom of sorts. The whip breaks the sound barrier, thus, it was broken on horseback.logicmath
Every day, Jack arrives at the train station from work at 5 pm. His wife leaves home in her car to meet him there at exactly 5 pm, and drives him home. One day, Jack gets to the station an hour early, and starts walking home, until his wife meets him on the road. They get home 30 minutes earlier than usual. How long was he walking? Distances are unspecified. Speeds are unspecified, but constant. Give a number which represents the answer in minutes.
The best way to think about this problem is to consider it from the perspective of the wife. Her round trip was decreased by 30 minutes, which means each leg of her trip was decreased by 15 minutes. Jack must have been walking for 45 minutes.logicshort
What is the significance of the following: The year is 1978, thirty-four minutes past noon on May 6th.
The time and month/date/year are 12:34, 5/6/78.logicmystery
You have two sand hourglasses, one that measures exactly 4 minutes and one that measures exactly 7 minutes. You need to measure out exactly 2 minutes to boil an egg. Using only these two hourglasses, how can you measure out exactly 2 minutes to boil your egg?
Flip over both hourglasses at the same time.
After 4 minutes, the 4-minute hourglass will be done, and there will be 3 minutes left in the 7-minute hourglass. Immediately flip the 4-minute hourglass over again.
After 3 more minutes, the 7-minute hourglass will be done, and there will be exactly 1 minute left in the 4-minute hourglass. Immediately flip the 7-minute hourglass over again.
After 1 more minute, the 4-minute hourglass will be done again, and there will be exactly 6 minutes left in the 7-minute hourglass. Immediately flip over the 4-minute hourglass.
After 4 more minutes, the 4-minute hourglass will be done again, and there will be exactly 2 minutes left in the 7-minute hourglass. At this point, put your egg in the boiling water. When the 7-minute hourglass is done, it will have been exactly 2 more minutes, and your egg will have boiled just right.logicprobability
Your enemy challenges you to play Russian Roulette with a 6-cylinder pistol (meaning it has room for 6 bullets). He puts 2 bullets into the gun in consecutive slots, and leaves the next four slots blank. He spins the barrel and hands you the gun. You point the gun at yourself and pull the trigger. It doesn't go off. Your enemy tells you that you need to pull the trigger one more time, and that you can choose to either spin the barrel at random, or not, before pulling the trigger again. Spinning the barrel will position the barrel in a random position.
Assuming you'd like to live, should you spin the barrel or not before pulling the trigger again?
You are better off shooting again without spinning the barrel.
Given that the gun didn't fire the first time, it was pointing to one of the four empty slots. Because your enemy spun the cylinder randomly, it would have been pointing to any of these empty slots with equal probability. Three of these slots would not fire again after an additional trigger-pull, and one of them would. Thus, by not spinning the barrel, there is a 1/4 chance that pulling the trigger again would fire the gun.
Alternatively, if you spin the barrel, it will point to each of the 6 slots with equal probability. Because 2 of these 6 slots have bullets in them, there would be a 2/6 = 1/3 chance that the gun would fire after spinning the barrel.
Thus, you are better off not spinning the barrel.logic
Handel has been killed and Beethoven is on the case. He has interviewed the four suspects and their statements are shown below. Each suspect has said two sentences. One sentence of each suspect is a lie and one sentence is the truth. Help Beethoven figure out who the killer is.
Joplin: I did not kill Handel. Either Grieg is the killer or none of us is.
Grieg: I did not kill Handel. Gershwin is the killer.
Strauss: I did not kill Handel. Grieg is lying when he says Gershwin is the killer.
Gershwin: I did not kill Handel. If Joplin did not kill him, then Grieg did.
Who is the killer?
Strauss is the one who killed Handel. You need to take turns assuming someone is the killer; that means everyone's second sentence is a lie. If Joplin was the killer, Grieg's lie mixed with Strauss' counteracts the other. If Grieg was the killer, Gershwin would need to be a killer too. If Gershwin was the killer, Gershwin would need to be a killer too. If Gershwin was the killer, Grieg and Strauss counter each other again, but with Strauss, everything would fit in. logic
A man eats dinner, goes up to his bedroom, turns off the lights, and goes to sleep. In the morning, he wakes up and looks outside. Horrified at what he sees, he hurls himself out his window to his death.
Why does he do this?
The man was a lighthouse operator. He wasn't supposed to turn off his lights. When he wakes up in the morning, he sees a giant ship that has crashed into the land, causing much catastrophe. Unable to go on, he decides to take his own life.