# Take a Challenge

## The Countdown

You have a string-like fuse that burns in exactly one minute. The fuse is inhomogeneous, it may burn slowly, then quickly, then slowly, and so on. You have a match and no watch. How can you measure exactly 30 seconds?

## How Much Will You Spend?

You receive eight balls. They are identical except that one is heavier than the rest. You have access to a scale but it cost \$10 per use. What is the least amount you can spend to find which ball is the heaviest and how?

## Can you Correct The Labels?

There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly? Which box should you choose from?

## How Long To Reach The Top?

A snail is climbing a 10-foot flag pole. He climbs up three feet every 45 minutes. He likes to take naps for 15 minutes after climbing. While sleeping, he slides down by one foot. How long until he reaches the top of the pole?

## Can You Crack The Safe?

You're trying to crack a three-number dial safe. Without knowing the combination numbers, what is the maximum number of trials required to open the safe? A trial is considered a full three-number combination. There are 40 numbers on this safe. To enter a combination you start with the dial at zero and turn counter-clockwise until the first number, then clockwise back to zero, then clockwise to the second number, then counter-clockwise back to zero, and finally counter-clockwise to the third number. Upon the correct combination, the safe will spring open.

## How Many Degrees?

What is the angle (if any) between the hour and minute hands of a clock when the time is 9:45?

## Rapidly Growing Lilies

You start with a single lily pad sitting on an otherwise empty pond. You are told that the surface area of the lily doubles every day and that it will take 30 days for the single lily to cover the surface of the pond. | If instead of one lily pad you start with eight lily pads (each identical in characteristics to the original lily), how many days will it take for the surface of the pond to be covered? Assume that they don't overlap each other.

## Can You Get a Matching Pair?

Your sock drawer contains 11 red socks and 15 blue socks. Your light isn't working and you must select your socks without seeing them. What is the minimum number of socks you need to take from your drawer and carry to a well-lit room to guarantee at least a matching pair?

## How Many Micro-Cubes Have Fallen?

Picture a 10 x 10 x 10 "macro-cube" floating. The macro-cube is composed of 1 x 1 x 1 "micro-cubes", all stuck together. Through some damage, the exposed (outermost) layer of micro-cubes loosen and fall to the ground. How many micro-cubes are on the ground?

## How Efficiently Can You Cross A Bridge?

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

## There is an easy way and a HARD way to do this

What is the sum of integers from 1 to 100? Integers are whole numbers only.