2. Write the numbers from 1 to 8 into the squares, so that the squares with consecutive numbers do not touch (neither edges nor corners).

3. Try to place all the numbers from 1 to 9 in the right place in the grid. OddEven Multiple of 3 Prime Square Factor of 168 4 2 91 3 6 5 7 8

4. FOUR is an even number with an even number of letters Primes: 2 3 5 7 11 13 17 19 23 29 31 37 Squares: 1 4 9 16 25 36 49 64 81 100 121 144 Cubes: 1 8 27 64 125 216 343 512 729 1000 1331 1728 Triangulars: 1 3 6 10 15 21 28 36 45 55 66 78 Evens: 2 4 6 8 10 12 14 16 18 20 22 24 Odds: 1 3 5 7 9 11 13 15 17 19 21 23

5. A married couple has two children. Given that the probability of having boys and girls are equal, and also given that one of their children is a girl, what is the chance that the other will also be a girl?

6. A group of 100 soldiers suffered the following injuries in a battle: 70 soldiers lost an eye, 75 lost an ear, 85 lost a leg, and 80 lost an arm. What is the minimum number of soldiers who must have lost all 4? 30 25 15 20 10

7. A clock is broken into two pieces. The numbers on each piece add up to the same answer. Where did the clock face break? 39

8. If I went halfway to a town 60 km away at the speed of 30 km/hour, how fast do I have to go the rest of the way to have an average speed of 60 km/hour over the entire trip? It’s impossible. You need to complete the 60km distance in one hour, and you’ve already been on the road for an hour.

9. Right now Mummy is 21 years older then her child. In 6 years her child will be 5 times younger than she. Where is Daddy? Child’s age = C Mummy’s age = M = C + 21 5(C + 6) = M + 6 5(C + 6) = C + 21 + 6 5C + 30 = C + 27 4C = -3 C = -3/4

10. This pool has 4 taps. Tap A takes 1 day to fill the pool. Tap B takes 2 days. Tap C takes 3 days. Tap D takes 6 days. How long would it take to fill the pool if all 4 taps were running simultaneously? Tap A: 1 pool per day Tap B: ½ pool per day Tap C: 1/3 pool per day Tap D: 1/6 pool per day Altogether: 6/6 + 3/6 + 2/6 + 1/6 = 12/6 = 2 pools per day Time taken to fill one pool at this rate: ½ a day

11. Diophantus This tomb tells scientifically the measure of his life. He was a boy for a sixth of his life; after a further twelfth, his cheeks acquired a beard; He was married after a further seventh, and in the fifth year after his marriage he fathered a son. Alas, his son died at only half the span of his father’s life, and after finding comfort in maths for a further 4 years, he passed away.

12. These cylindrical vessels (of negligible thickness) are placed one inside the other, then filled with water, then removed from each other. Which one contains the most water?