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**Round 1**

1. What is the largest street number of any building in England?

2. Part of New York City has a grid pattern, with the north-south streets called First Avenue, Second Avenue, and so on, and the east-west ones called 1st Street, 2nd Street, and so on. What is the highest numbered street?

3. And the highest numbered avenue?

4. And the only fraction-numbered avenue?

5. A street has houses numbered 1 to 199. How many of each digit – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 – do you need to make the street-number signs for nos.1 to 99?

6. How many for nos.100 to 199?

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**Round 2**

1. I fire a gun horizontally and simultaneously drop a bullet. Which hits the ground first, the bullet fired from the gun, or the bullet I dropped?

2. You have to measure exactly 4 litres of water, but you only have a 3-litre bottle and a 5-litre bottle. How do you do it?

3. You start walking north and you walk in a straight line for two kilometres. When you look at the map, you discover that you actually walked one kilometre north and one kilometre south. How is this possible?

4. I can tile my floor without gaps using identical tiles which are regular polygons (all sides and angles the same). How many sides can the tiles have?

5. Everyone in France always shakes hands with a friend when meeting them for the first time in a particular day. You and five friends meet for the first time one day. How many handshakes?

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**Round 3**

1. How can you flip this triangle upside down by moving only three coins?

2. How can you make seven squares here by moving only two matches?

3. How many squares, altogether, of different sizes, are there here?

4. And here?

5. And here?

6. And in a 10×10 grid?

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**Round 4**

1. If all seven billion people in the world stood as close together as in a crowded Tube train, what area would they fit into? The equivalent of Europe? Of England? Of south-east England? Of London? Of Southwark?

2. About how many times in a year do you breath in and out?

3. About how many words a day does the average person say?

4. About how many pizzas are sold in the whole world per year?

5. About how many mobile phones are there in the world?

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**Round 5**

1. Why are there 60 minutes in an hour, and 60 seconds in a minute?

2. Why are there 360 degrees in a circle?

3. Why are there 1024 bytes in a kilobyte?

4. Why can a cat survive a big fall but an elephant can’t?

5. During the French Revolution, as well as introducing the metric system for lengths and weights, the revolutionary authorities also decreed that a right angle would now be 100 degrees instead of 90. The metric system has spread from France to the whole world, but the 400 degree circle did not stick. Why not?

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**Round 6**

1. This man pioneered probability theory, invented proof by induction, was a famous philosopher, and had a computer programming language very popular in the 1980s and 90s named after him, but is even better known for a triangle named after him. Who is he?

2. This man invented differentiation and most of the main laws of physics commonly used today, and has also been called the second nastiest person ever to come out of Grantham. Who is he?

3. This woman is called the Mother of Modern Algebra, yet she could only ever get a junior lecturer job at university, and she was sacked even from that in 1933 because she was Jewish and left-wing. Who is she?

4. This Iranian mathematician was the first woman to win the Fields Medal, the equivalent of the Nobel Prize for maths, and there’s a display about her work in 2B6. Who is she?

5. This man worked out the four-dimensional maths for Einstein’s theory of relativity, and there’s a display featuring him in 2B6. Who is he?

6. This man designed the basic architecture for electronic computers, only slightly modified today, and made many advances in maths. He was also the only famous mathematician in history to turn up to work each day in a suit and tie. Who is he?

7. The biggest number ever used in a mathematical proof is named after this man – “So-and-so’s number” – and he’s well-known for work in Ramsey theory. He used to work as a circus performer, and is still an expert juggler. Who is he?

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**Round 7**

1. You’re arranging a party, and ten people promise each to take responsibility for one part of the organisation. If any one person fails or delays too much, then the party will have to be cancelled. All ten people are 90% reliable, i.e. there is probability 0.9 that they will do their job reasonably on-time. What’s the risk of having to cancel the party?

2. In a game show a winner gets to choose from three boxes, one of which contains a good prize and the other two a goat (and you don’t want a goat). You choose. The game show host opens one of the boxes you’ve not chosen to show it contains a goat, and gives you a chance to swap choices. Should you swap?

3. You have a choice between a million pounds and the amount of money you could get by putting 1p on the first square of a chessboard, 2p on the second, 4p on the third, 8p on the fourth, and so on. Which should you choose?

4. You have only six socks, some black, some white, and you pick a pair in the dark. The probability of you getting a white pair is ⅔. What’s the probability of you getting a black pair?

5. Work out the missing area without using any fractions in your working.

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1.1 – 2679 Stratford Road, Hockley Heath, Solihull B94 5NH. The USA has bigger street numbers, and the biggest seems to be 107800

1.2 – 271st Street

1.3 – 165th Avenue

1.4 – Six and a half avenue

1.5 – 9×0, and 20× each other digit, for nos.1-99

1.6 – 120×1, and 20 times each other digit, for nos.100-199

Round 2 questions

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2.1 – They hit the ground simultaneously

2.2 – a. Fill the 3-litre bottle and pour it into the empty 5-litre bottle. b. Fill the 3-litre bottle again, and pour enough to fill 5-litre bottle. This leaves exactly 1 litre in the 3-litre bottle. c. Empty the 5-litre bottle; pour the remaining 1 litre from the 3-litre bottle into the 5-litre bottle. d. Fill the 3-litre bottle and pour it into the 5-litre bottle.

2.3 – You started one kilometre south of the North Pole

2.4 – 3, 4, or 6. You can tile without gaps with some irregular pentagons (15 different sorts of pentagons, it is thought, but it’s not proved there are no more). But it is impossible to tile with convex polygons of seven or more sides

2.5 – 15

Round 3 questions

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3.1 –

3.2 –

3.3 – 5

3.4 – 14

3.5 – 30

3.6 – 385

Round 4 questions

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Round 4

4.1 – London

4.2 – Seven million

4.3 – 16,000

4.4 – Five billion

4.5 – 7.2 billion. Some serious investigators reckon there are more mobile phones in the world than toothbrushes.

Round 5 questions

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Round 5

5.1 – Because in ancient Babylon they had numbers to base 60, not 10

5.2 – Because in ancient Babylon they thought there were about 360 days in a year

5.3 – Because computers use base 2, and 2^{10}=1024, not 1000

5.4 – Because weight increases by the cube of an animal’s size and area (e.g. of cross-section of leg) only by the square. For the same reason, large birds can’t fly. (Even eagles, apparently, cannot strictly speaking fly, but only glide on warm-air currents).

5.5 – It makes the angles of an equilateral triangle 66⅔ degrees. 360 has the advantage of more divisibility.

Round 6 questions

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6.1 – Blaise Pascal

6.2 – Isaac Newton

6.3 – Emmy Noether

6.4 – Maryam Mirzakhani

6.5 – Hermann Minkowski

6.6 – John von Neumann

6.7 – Ron Graham

Round 7 questions

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7.1 – 65%

7.2 – yes. P(prize in box you first picked)=⅓. P(prize in box host opened)=0. P(prize in other box)=⅔.

7.3 – The pennies on the chessboard.

7.4 – Zero

7.5 – 20. The width of the top bit is 11, so the width of the bottom bit is 10, and the total area of the bottom bit is 60.