1. Pizza Slices
What is the maximum number of slices of pizza you can make with just three straight line?

2. Pizza Slices
Answer: 7 2 1 3 7 4 6 5

3. Constellation
Can you arrange four stars such that all are equidistant from each other?

4. Constellation
Answer: In a tetrahedron made of equilateral triangles.

5. Utilities
Three houses need to have water, electricity and gas supplied to them. The only problem is that the pipes and wires cannot cross! Can you supply all three utilities to the houses without any of the lines crossing?
ELECTRICITY
WATER
GAS

6. Utilities
Answer: It’s impossible in our spherical world!

7. The Fake Coin
You have 9 coins but one of them is fake. The fake coin weighs slightly less than the real coins. You have a set of balance scales to help you.
What is the smallest number of weighings
needed to correctly determine the fake
coin?

8. The Fake Coin
Answer: 2!
Weigh two sets of three coins. Either one set will weigh more than the other, in which case the fake coin is in that set, or they’ll balance and the fake coin is in the set not on the scales
Repeat the process above, weighing two of the three coins from the set left to determine the fake coin!

9. The Label Mix-Up Red & White White Red
Three boxes contain bottles of wine. One box contains just red wine, one just white wine and the other a mix of red and white wines. However, all the labels are on the wrong boxes.
I can show you one bottle from one box and from that you need to put the correct labels on the correct boxes.
Red & White
White
Red

10. The Label Mix-Up
Answer:
Red & White
Red
White

11. The Farmer’s Last Theorem
The deeds for a farm are locked in a box. Your great grandfather buried the keys somewhere in the orchard. He left some instructions on how to find the key that will open the box.
The instructions read as follows:
“I tied my horse to an apple tree, walked to the large oak tree. Turned 90 degrees left, and walked the same distance again. This is a spot where I left a beehive! I then walked from the horse to the small oak tree. Turned 90 degrees right and walked the same distance away again. This is where I placed the second beehive. The key to open the box containing the deeds to the farm is buried beneath the tree that is exactly halfway between the two beehives.”
But that was three generations ago. The beehives have since been removed and the horse has been dead for years! Can you still find the key?!

12. K J I H G F E D C B A

13. K J I H G F E D C B A

14. K J I H G F E D C B A

15. K J I H G F E D C B A

16. K J I H G F E D C B A

17. Student Problem
A student has a problem. He got a bit tipsy last night and his ‘friends’ stole his clothes! His friends are located at five points in a city. Can you determine where it is best for the student to locate himself so that his friends have to travel the combined least distance possible?
N.B: His friends cannot walk through buildings so must follow the streets (grid lines)

18. 8 7 5 6 5 2 4 3 2 2 1 1 3 1 2 3 4 5 6 7 8

19. 8
13 People, so need to know the position of the 7th person on the x and y axes.
This is 5 on the x-axis and 5 on the y-axis.
Anywhere else and you save distance for 6 people but increase it for 7! 7 5 6 5 X 2 4 3 2 2 1 1 3 1 2 3 4 5 6 7 8

20. The Blood-Sucker Challenge
Three vampires and three fair maidens want to go up to the rooftop bar but there is only one lift and it only fits two people.
If the number of vampires ever exceeds the number of maidens, the maidens will be devoured by the vampires.
Each time two go up in the lift, one must come back down.
How many moves does it take to get all six up to the rooftop bar without any of the maidens being eaten?

21. The Blood-Sucker Challenge
BOTTOM
TOP
MOVEMENT
3V, 3M
2V Up
1V, 3M 2V
1V down
2V, 3M 1V 3M 3V
2M up
1V, 1M
2V, 2M
1V, 1M down
Answer: 11

22. The 4 Litre Challenge 8L 5L 3L
You have 3 bottles: an 8L, 5L and 3L bottle.
The 8L bottle is full of oil, the other two are empty.
Can you use the bottle to split the 8L of oil into two 4L quantities? If so, what is the fewest number of moves needed to do so? 8L 5L 3L

23. The 4 Litre Challenge Answer: 7 5L 6L 4L 6L 3L 3L 5L 4L 3L 3L 2L 2L 2L
1) Pour 5L into the 5L jar. 6L 4L 6L 3L 3L 5L 4L 3L 3L 2L 2L 2L 2L 1L
2) Pour 3L from the 5L jar into the 3L jar.
3) Pour the 3L jar into the 8L jar.
4) Pour the 2L in the 5L jar into the 3L jar.
5) Pour 5L from the 8L jar into the 5L jar.
6) Pour 1L from the 5L jar into the 3L jar.
7) Pour the 3L jar into the 8L jar!

24. On Your Bike
The Tour de France is designing a new course. They want to visit all of the villages shown on the map, but they only want to use each road once.
Where should the race start and finish?

25. On Your Bike
Answer: You must start and finish at a village with an odd number of roads coming from it.
So start/finish at Blagnac and Bonneval.