Brain teasers

These mini-puzzles are a small collection of teasers to make you think. Don't reveal the answers until you've thought about them for a bit!

TV game show

Imagine you're on a game show on tv, and you're offered the choice of three prizes behind closed doors. One of the prizes is very valuable (usually a car), and behind the other two doors are worthless prizes (often goats). You don't know what's behind which door, but the game show host does. You choose a door (hoping to get the car). The host, instead of opening your selected door, raises the tension by opening one of the other two doors instead, behind which he knows there is a goat. Then he offers you the choice - do you stick with your previously-selected door, or do you switch to the other, still closed, door?

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Average speed

You plan a bicycle journey, from your home to the next town and back again on the same route. You would like to get an overall average speed of 20 km/h. After setting off, you get delayed, so that when you reach the town, your average speed is only 10 km/h. How fast do you have to cycle on the return journey so that your average speed for the whole trip is 20 km/h?

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Hot coffee

You make a cup of coffee, but before you add the milk you realise that it's too hot to drink. If you want the coffee to cool down to drinkable temperature as soon as possible, should you add the milk now or later?

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This one is more mathematical. You start with three numbers, and you try to make the number 6 by drawing mathematical symbols between the numbers to make a sum. What is a mathematical symbol? Well, for starters there are the normal add, subtract, multiply and divide. For some you might need to add brackets ( ), and for the harder ones you might need to resort to additional operations. But you can't draw any extra numbers in there, only symbols.

Here are the sums, and the first one is done for you.

1     1     1 = 6   (difficult)
2 + 2 + 2 = 6   (easy)
3     3     3 = 6   (easy)
4     4     4 = 6   (medium)
5     5     5 = 6   (medium)
6     6     6 = 6   (easy)
7     7     7 = 6   (medium)
8     8     8 = 6   (difficult)
9     9     9 = 6   (medium)

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