## Out of Place

Which of the numbers below is out of place and why?

1011, 2223, 3940, 5646, 8910

Every number except 5646 can be split into a sequence of consecutive numbers: 1011~10-11, 2223~22-23, 3940~39-40, 8910~8-9-10.

## Two Games at Once

The Devil offers you a deal – you have to play two games of chess simultaneously against the two best GrandMasters in the world, one with black pieces and one with white pieces. If you win at least 1 point from the two games, you will get whatever your heart desires, if you don’t – you will go straight to Hell. Would you accept the challenge?

Accept the challenge. You can easily get 1 point by just repeating the moves of your opponents. For example, if the white GrandMaster plays e4, then you play e4 against the black GrandMaster. If the back GrandMaster plays e5, then you play e5 against the white GrandMaster and so on.

## Least Likely

Sarah lives in UK. Which of these statements is least likely:

1. Sarah speaks English;
2. Sarah eats baby pandas;
3. Sarah speaks English and eats baby pandas.

The answer is 3. This is because statements 1. and 2. are more general than statement 3. and therefore more likely to be true.

## Measuring Scale

You have 10 unlimited piles of balls and one measuring scale. All balls in a pile have the same weight which is an integer between 1 and 9 grams. How many measurements do you need in order to find the weight of the balls in every pile?

You need only one measurement – take 1 ball from pile 1, 10 balls from pile 2, 100 balls from pile 3, etc, and measure their total weight. The first digit of the number shown on the scale determines the weight of the balls in the 10th pile, the second digit determines the weight of the balls in the 9th pile and so on.

## Wine and Water

You have two 1 liter mugs – one of them halfway filled with water and the other one halfway filled with wine. You pour 300ml water from the first mug into the second one, stir it well, then pour 300ml of the mix from the second mug back to the first one. Now, do you have more water in the first mug than you have wine in the second one?

If you have X ml water in the first mug, then in the second mug you have 500-X ml water and X ml wine. Therefore you have exactly as much water in the first mug as you have wine in the second one.

## Hourglasses

You have a 7-minute hourglass and an 11-minute hourglass. How can you measure exactly 15 minutes with them?

Turn both hourglasses upside down. When the time of the 7-minute hourglass runs out, turn it upside down. When the time of the 11-minute hourglass runs out, turn the 7-minute hourglass upside down again. Finally, when the time of the 7-minute hourglass runs out, exactly 15 minutes will have been passed.

## Slowest Horse

Two friends made a bet whose horse is slower. After wondering for days what is the fastest and fairest way to figure out who wins the bet, they finally decided to ask a famous wise hermit for help. Upon giving them his advice, the two friends jumped on the horses and started racing back to the city as fast as they could. What did the hermit say?

He told them to switch their horses and whoever gets to the city first will win the bet.

## Ancient Coins

Suppose I show you two ancient coins. The first one is dated 51 B.C., the second one is marked George I. Which one is counterfeit?

Both of them. People who lived 51 years before Christ didn’t know about Jesus yet. Also, when king George I was ruling, he was the first king with this name, and thus was regarded simply as George.

## Funky Mate

Place only 2 rooks and 1 knight on the board, so that the Black player is mated.

You can place the rooks on c5 and e5, and the knight on f5.

## Mountain Hike

A man decides to climb a mountain. He starts at sunrise from the bottom of the mountain and arrives on the top at sunset. He sleeps there and on the next day he goes back the same way, descending at higher speed. Prove that there is some point of his path, on which the man will be at the same time on both days.

Imagine a second man who starts climbing from the bottom of the mountain on the second day and following the first hiker’s first day movements. At some point the first and the second hiker will meet each other, and this will be the point you are looking for.