Classic Brainteasers Flashcards
5 pirates are trying to decide to split 100 coins. The most senior pirate will propose a solution and then all the pirates (including most senior pirate) will vote. If 50%+ agree, the gold is divided as proposed. If not, the most senior pirate is tossed overboard the process repeats. How will the coins be divided in the end?
For any 2n +.1 pirate case, the most senior pirate will offer pirates #1, #3, …, 2n -1 one coin and keep the rest for himself.
100 tigers and 1 sheep are on an island where if the tiger eats the sheep, it will be turned into a sheep itself. Will the sheep be eaten?
If there is an even number of tigers, the sheep won’t be eaten.
4 people need to cross a river on a dark bridge with one lantern, and the only way to cross is either singly or in pairs, moving at the speed of the slower person. The time taken by each person is A > B > C > D. What is the minimum time taken to cross?
A & B should cross together, but not at the first crossing. It should go CD (send back D), AB (send back C), then CD to get the minimal time.
You have a set of dates for a friend’s birthday. One person A gets the month, and one person B gets the day. The first person says ‘I don’t know the birthday, and B doesn’t know it either.’ Then B replies ‘I didn’t know the birthday, but now I know it.’ and then person A knows it too. What’s the birthday?
Consider uniqueness to eliminate the possible days.
A casino game uses a normal deck where you turn over two cards at a time. If both are black, they go to the dealer; if both are red, they go to you; if one is black and one is red, they are discarded. Should you play?
An equal number of black and red cards will be discarded, and the number of red cards left for you and the black cards left for the dealer remain the same. The dealer always wins.
You have 2 ropes that each take an hour to burn but with different densities along the rope. How do you measure 45 mins?
Burn one rope at both ends and the other at 1 end. The first rope will be done in half an hour. Once it’s done, the second rope becomes a half hour rope and you can burn it at the other end too to make it a 15-min rope.
You have a set of identical balls, except for a defective one that is either heavier or lighter than the rest. How do you find the defective ball in 3 measurements?
If you know the ball is heavier or lighter, you can identify the defective ball among up to 3^n balls in no more than n measurements. If you don’t know, you can find the ball among up to (3^n -3)/2 balls in no more than n measurements.
How many trailing zeros are in 100! (factorial)
Each pair of 2 and 5 will give a trailing zero, and since there are more 2’s than 5’s in the prime number decomposition, the 5’s will determine the number of trailing zeros. 20 numbers are divisible by 5 (between 1 and 100) and 4 of them are divisible by 5^2, so there will be 24 trailing zeros.
There are 25 horses and 5 lanes. How many races do you need to determine the 3 fastest horses?
7 - five for the group split evenly, 1 with the original winners, and 1 to determine the third place from what remains.
If x^x^x^x^x… = 2, what is x?
Square root of two (n root of n for whatever the infinite series equals)
Can you pack 53 bricks of dimensions 1 x 1 x 4 into a 6 x 6 x 6 box?
Short answer - no. Decompose the 6 x 6 x 6 box into groups of 2 x 2 x 2 (smallest unit that can contain at least part of the 1 x 1 x 4 box). It can contain 27 of these smaller boxes, so either 13 black/14 white or vice versa. But one 2 x 2 x 2 can only contain up to 4 of the 1 x 1 x 4 boxes, so for the color with 13, can only have up to 52 boxes and you can’t place the 53rd box.
You have two custom dice made to show the dates of the calendar. What numbers do you have on each die?
1 2 0 3 4 5
1 2 0 3 4 5
You have two doors with two guards, one in front of each door. One always tells the truth and one always lies. How do you pick the door you want?
Ask the guard ‘Would the other guard say that you are guarding the door to the offer?’ If the answer is ‘yes’ choose the other door. If the answer is ‘no’ choose his door.
How do you send a secured message in a box to a friend?
Send it with your lock, he sends it back with his lock. You unlock your lock and send it back. He can then unlock his lock.
A bag has 20 blue balls and 14 red balls. Each time you take out two balls randomly (assume each ball in the bag has equal probability of being taken). You don’t put them back. If both balls have the same color, you add a blue ball. If they have different colors, you ad a red. What will be the color of the last ball in the bag? What if it’s 20 blue and 13 red?
If it’s an even number of red balls, blue will remain. If it’s an odd number of red, red will remain.
BB: (B, R) → (B-1, R)
RR: (B, R) → (B+1, R-2) (since red only decreases by 2, if the number of red balls is even, you run out of them)
BR: (B, R) → (B-1, R)
