Difficult logic riddles

logicsimpleclean

Two convicts are locked in a cell. There is an unbarred window high up in the cell. No matter if they stand on the bed or one on top of the other they can't reach the window to escape. They then decide to tunnel out. However, they give up with the tunnelling because it will take too long. Finally one of the convicts figures out how to escape from the cell. What is his plan?
His plan is to dig the tunnel and pile up the dirt to climb up to the window to escape.
73.90 %
78 votes
logicmath

Assume: 5+3+2 = 151022 9+2+4 = 183652 8+6+3 = 482466 5+4+5 = 202541 Then; 7+2+5 = ?
143547 Explanations: Multiplication of the 1st & 2nd numbers, 5*3 = 15; 9*2 = 18…thusly, 7*2 = 14 Multiplication of the 1st & 3rd numbers, 5*2 = 10; 9*4 = 36…thusly, 7*5 = 35; Multiplication of the 1st & the sum of the 2nd & 3rd numbers. The generated result is reduced by the value of the 2nd number, …thusly, 7*(2+5) = 49 - 2 = 47
73.64 %
59 votes
logicstoryclean

One day, Emperor Akbar posed a question to Birbal. He asked him what Birbal would choose if he offered either justice or a gold coin. "The gold coin," said Birbal without hesitation. On hearing this, Akbar was taken aback. "You would prefer a gold coin to justice?" he asked, not believing his own ears. "Yes," said Birbal. The other courtiers were amazed by Birbal's display of idiocy. They were full of glee that Birbal had finally managed himself to do what these courtiers had not been able to do for a long time - discredit Birbal in the emperor's eyes! "I would have been disappointed if this was the choice made even by my lowliest of servants," continued the emperor. "But coming from you it's not only disappointing, but shocking and sad. I did not know you were so debased!" How did Birbal justify his answer to the enraged and hurt Emperor?
"One asks for what one does not have, Your Majesty." said Birbal, smiling gently and in quiet tones. "Under Your Majesty´s rule, justice is available to everybody. But I am a spendthrift and always short of money and therefore I said I would choose the gold coin." The answer immensely pleased the emperor and respect for Birbal was once again restored in the emperor's eyes.
73.59 %
121 votes
logicmath

What is the smallest number, that can be expressed as the sum of the cubes of two different sets of numbers?
Hardy-Ramanujan discovered 1729 as a magic number. Why 1729 is a magic number? 10^3 + 9^3 = 1729 and 12^3 + 1^3 = 1729 Taxicab number Ta(2)
73.31 %
85 votes
logicstorycleansimple

A wise man lived on a hill above a small town. The townspeople often approached him to solve their difficult problems and riddles. One day, two lads decided to fool him. They took a dove and set off up the hill. Standing before him, one of the lads said "Tell me, wise man, is the dove I hold behind my back dead or alive?" The man smiled and said "I cannot answer your question correctly". Even though the wise man knew the condition of the dove, why wouldn't he state whether it was dead or alive?
The man told the two lads, "If I say the dove is alive, you will the bird and show me that it is dead. If I say that it is dead, you will release the dove and it will fly away. So you see I cannot answer your question. Search: Schrödinger's cat
73.27 %
128 votes
logicmath

There are 5 pirates in a ship. Pirates have hierarchy C1, C2, C3, C4 and C5. C1 designation is the highest and C5 is the lowest. These pirates have three characteristics: a. Every pirate is so greedy that he can even take lives to make more money. b. Every pirate desperately wants to stay alive. c. They are all very intelligent. There are total 100 gold coins on the ship. The person with the highest designation on the deck is expected to make the distribution. If the majority on the deck does not agree to the distribution proposed, the highest designation pirate will be thrown out of the ship (or simply killed). The first priority of the pirates is to stay alive and second to maximize the gold they get. Pirate 5 devises a plan which he knows will be accepted for sure and will maximize his gold. What is his plan?
To understand the answer,we need to reduce this problem to only 2 pirates. So what happens if there are only 2 pirates. Pirate 2 can easily propose that he gets all the 100 gold coins. Since he constitutes 50% of the pirates, the proposal has to be accepted leaving Pirate 1 with nothing. Now let's look at 3 pirates situation, Pirate 3 knows that if his proposal does not get accepted, then pirate 2 will get all the gold and pirate 1 will get nothing. So he decides to bribe pirate 1 with one gold coin. Pirate 1 knows that one gold coin is better than nothing so he has to back pirate 3. Pirate 3 proposes {pirate 1, pirate 2, pirate 3} {1, 0, 99}. Since pirate 1 and 3 will vote for it, it will be accepted. If there are 4 pirates, pirate 4 needs to get one more pirate to vote for his proposal. Pirate 4 realizes that if he dies, pirate 2 will get nothing (according to the proposal with 3 pirates) so he can easily bribe pirate 2 with one gold coin to get his vote. So the distribution will be {0, 1, 0, 99}. Smart right? Now can you figure out the distribution with 5 pirates? Let's see. Pirate 5 needs 2 votes and he knows that if he dies, pirate 1 and 3 will get nothing. He can easily bribe pirates 1 and 3 with one gold coin each to get their vote. In the end, he proposes {1, 0, 1, 0, 98}. This proposal will get accepted and provide the maximum amount of gold to pirate 5.
73.25 %
76 votes
cleanlogicmathsimple

Create a number using only the digits 4,4,3,3,2,2,1 and 1. So I can only be eight digits. You have to make sure the ones are separated by one digit, the twos are separated by two digits the threes are separated with three digits and the fours are separated by four digits.
41312432.
73.23 %
115 votes
logiccleansimple

Six jugs are in a row. The first three are filled with coke, and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?
Move and then pour all coke from second glass to fifth glass.
73.22 %
67 votes