Leap Logic 4

Think of a number. Multiply it by 2 and add 4. Multiply the result by 0.5 and add 3, and then subtract the original number. I know what number you have left. What must it be?

You are on a train with 4 other people, one of whom stole your wallet!

Here are their statements, and exactly 3 of them are lies:

Person 1 said, "2 stole the wallet."

Person 2 said, "3 didn't steal it."

Person 3 said, "I didn't steal it."

Person 4 said, "3 stole your wallet."

Who actually stole your wallet?

• Person 1

• Person 2

• Person 3

• Person 4

Suppose you have 8 watermelons that are exactly the same in appearance. They are equal in weight except for one, which is heavier than the others. You want to find the heaviest one by using a two-pan balance. Each pan can hold any number of watermelons, and the only items that you can place in the pans are watermelons.

In the worst case scenario, how many times do you have to use the two-pan balance?

You go into your garage and find a pile of 100 batteries (all the same type). You happen to know that half of them are good and half are bad, but you can't tell which is which. You have a flashlight which uses two batteries, and requires both to work in order to turn on.

In the worst case scenario, with an optimal strategy, what is the minimum number of times you will need to put batteries into the flashlight before you can guarantee to get a working pair in the flashlight?

Details and Assumptions:

The flashlight either turns on or it doesn't, i.e. there is no way to distinguish between one of the two working and neither one working.

Your answer should be the number of "flashlight loadings" you will need to actually get your flashlight working, not just how many you would need to identify two good batteries.

You are playing a game of Nim with an opponent by drawing blocks from the pile above. (The picture is a side view; gravity applies.) On each turn a player can take a block and any blocks that it supports. For example taking block C would also take D and E.

The person who takes the last block -- block A -- loses.

It's your turn. Which block should you take if you want to win? (Remember, the one to take the last block loses.)

• B

• C

• D

• E

You have two light bulbs in a 100-story building. You want to find out what floor the bulb will break on, using the least number of drops.

It is X's turn. Can X win?

• Yes

• No

There are 50 bikes, each with a tank that holds enough gas to go 100 km. Using these 50 bikes, what is the maximum distance that you can go?