**Puzzle 1:** Distances from you to certain cities are written below.

BERLIN 200 miles

PARIS 300 miles

ROME 400 miles AMSTERDAM 300 miles

CARDIFF??? Miles

How far should it be to Cardiff?

**Solution: **100 miles. Each vowel is worth 300 and each consonant is worth -100. These are totaled in each city name to give the distance

**Puzzle 2:** If you throw me from the window,

I will leave a grieving wife.

Bring me back, but in the door, and

You’ll see someone giving life!

What am I?

**Solution: **“The letter ‘n’.

wiNdow – widow

door – doNor

**Puzzle 3:** The below is a number puzzle. It should be read left to right, top to bottom.

1

1 1

2 1

1 2 1 1

1 1 1 2 2 1

? ? ? ? ? ?

? ? ? ? ? ? ? ?

**Question 1:** What is the next two rows of numbers?

**Question 2:** How was this reached?

**Solution:** 3 1 2 2 1 1

1 3 1 1 2 2 2 1

Line 1 is ‘Two ones’ (2 1)

Line 2 then becomes ‘One two, and one one’ (1 2 1 1)

Line 3 therefore is ‘One one, one two and two ones’ (1 1 1 2 2 1)

Line 4 is ‘Three ones, two twos and one one’ (3 1 2 2 1 1)

Line 5 is ‘One three, one one, two twos and two ones’ (1 3 1 1 2 2 1 1)

**Puzzle 4:** In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

**Solution: **The answer is 2.

First, divide the coins into 3 equal piles. Place a pile on each side of the scale, leaving the remaining pile of 3 coins off the scale. If the scale does not tip, you know that the 6 coins on the scale are legitimate, and the counterfeit is in the pile in front of you. If the scale does tip, you know the counterfeit is in the pile on the side of the scale that raised up. Either way, put the 6 legitimate coins aside. Having only 3 coins left, put a coin on each side of the scale, leaving the third in front of you. The same process of elimination will find the counterfeit coin.

**Puzzle 5:** If you had a pizza with crust thickness ‘a’ and radius ‘z’, what’s the volume of the pizza?

**Solution:** pi * z * z * a