There are three playing cards in a row. There is a two to the right of a king. There is a diamond to the left of a spade. There is an ace to the left of a heart. There is a heart to the left of a spade. Identify the three cards.

SOLUTION

The cards are an Ace of Diamonds, a King of Hearts, and a Two of Spades.

There are 5 houses and each of them has a different color. Their respective owners have different heritages, drink different types of beverages, smoke different brands of cigarettes, and look after different types of pets. It is known that:

The Brit lives in the red house.

The Swede keeps dogs as pets.

The Dane drinks tea.

Looking from in front, the green house is just to the left of the white house.

The green house’s owner drinks coffee.

The person who smokes Pall Malls raises birds.

The owner of the yellow house smokes Dunhill.

The man living in the center house drinks milk.

The Norwegian lives in the leftmost house.

The man who smokes Blends lives next to the one who keeps cats.

The man who keeps a horse lives next to the man who smokes Dunhill.

The owner who smokes Bluemasters also drinks beer.

The German smokes Prince.

The Norwegian lives next to the blue house.

The man who smokes Blends has a neighbor who drinks water.

“If there is a vowel written on one side of a card, then there is an even number written on the other side.” How many of these four cards do you need to flip in order to check the validity of this sentence?

What would be the answer if you know that each card contains one letter and one number.

SOLUTION

You need to flip all cards except for the second one. If each card contains one letter and one number, then you need to flip only A and 7.

Two people play a game of NIM. There are 100 matches on a table, and the players take turns picking 1 to 5 sticks at a time. The person who takes the last stick wins the game. Who has a winning strategy?

SOLUTION

The first person has a winning strategy. First, he takes 4 sticks. Then every time the second player takes X sticks, the first player takes 6 – X sticks.

An evil warden holds you as a prisoner but offers you a chance to escape. There are 3 doors A, B, and C. Two of the doors lead to freedom and the third door leads to lifetime imprisonment, but you do not which door is what type. You are allowed to point to a door and ask the warden a single yes-no question. If you point to a door that leads to freedom, the warden does answer your question truthfully. But if you point to the door that leads to imprisonment, the warden answers your question randomly, saying either “YES” or “NO” by chance. Can you figure out a way to escape the prison?

SOLUTION

You can point towards door A and ask whether door B leads to freedom. If the warden says “YES”, then you open door B. It can not lead to imprisonment because this would mean that door A leads to freedom and the warden must have told you the truth. If the warden says “NO”, then you open door C. This is because either the warden lied, and then the imprisonment door is A, or he told you the truth, and then the imprisonment door is B.

You and eight of your team members are trying to escape the Temple of Doom. You are running through a tunnel away from a deadly smoke and end up in a large hall. There are four paths ahead, and exactly one of them leads to the exit. It takes 20 minutes to explore any of the four paths one way, and your group has only 60 minutes until the deadly smoke suffocates you. The problem is that two of your friends are known to be delirious and it is possible that they do not tell the truth, but nobody knows which ones they are. How should you split the group and explore the tunnels, so that you have enough time to figure out which is the correct path and escape the temple?

SOLUTION

You explore the first path. You send two of your teammates to explore the second path. You send the remaining six teammates in groups of three to explore each of the two remaining paths. If your path leads to the exit, then everything is good. Otherwise, you ask the two groups of three whether their paths lead to the exit. If in both groups everyone answers consistently, then nobody is lying, and you will escape. If in both groups there is a person whose answer is different from the others in the group, then the majority in both groups says the truth. Once again, you will know which path leads to the exit. Finally, if in exactly one of the groups everyone answers consistently, you ask the group of two. If the team members there answer consistently with each other, then they say the truth. You will have two groups which tell the truth and will know which path leads to the exit. If the answers of the teammates in the group of two differ, then in the inconsistent group of three the majority will be saying the truth. Again, you will be able to deduce which path leads to the exit.

King Arthur and his eleven honorable knights must sit on a round-table. In how many ways can you arrange the group, if no honorable knight can sit between two older honorable knights?

SOLUTION

The answer is 1024 ways, up to rotation around the table. To see this, notice that the youngest honorable knight must sit right next to King Arthur – there are two possible places for him. Then, the second youngest knight must sit right next to this group of two. Once again, there are two possible places for him. Continuing like this, we see that for all honorable knights, except for the oldest one, there are two possible spots on the table. Multiplying two to the power of ten out, we get 1024.

You had 10lbs of cucumbers, each of which consisted of 99% water. After leaving them in the sun, some of the water in the cucumbers evaporated. If the cucumbers ended up with 98% water in them, how much of their weight did they lose?

SOLUTION

The cucumbers lost half of their weight.

If the water was 99% of the total weight, the remaining substance must have weighed 0.1lbs. If after the evaporation the substance comprises 2% = 1/50 of the cucumbers, the total weight must be 50 x 0.1lbs = 5lbs.