First Series - coming soon!

The Puzzles

1. On a wine bottle I spot the word POLICE. Explain.

2. You and I argue, not so much as to whether the bottle is half full or half empty, but whether it is more or less than half full or empty. How can we resolve the question with no other vessels to hand?

3. I have 4 bottles, all labelled in rather negative terms.

The first label proclaims - 'I am not wine'

The second label says - 'I am not water'

The third label says - 'I am not gin'

The fourth bottle carries 2 statements on its label 

'I am not tonic', and, 'I am not water'.

Only 1 of these 5 assertions is true. How can I work out what's what?

4. How do 'consumed food' and a 'warning to golfers' amount to the same as 'also, gained victory' and 'German denial'?

5. What is the next number in this series?

2.1, 3.5, 3.3, 2.3, 1.3, 2.4, 2.5, 2.6, 1.8

6. Change:

GOAT to COWS, with 3 steps in between and with each step changing a single letter and at each stage making a valid word.

7. Now do something similar to change:

GRACES to FRANCE

Remember recreation may be involved.

8. To augment an old septic tank an octagenarian caretaker had the novel idea of decreasing its size. Mind you, the janitor was feeling unwell. How might he have been feeling?

9. In some far off country there is a dungeon with a 100 cells, and locked in each cell is a prisoner. As it is a high security prison there are also 100 guards, who are a bit eccentric. The locks on each door are of the type where if you turn the key once the door is locked, if you turn it again it is unlocked. It is nearly bedtime and the first prison guard, not realising that all the prison cells are already locked turns the key in every cell. The second guard comes along and he turns the key in every other cell ie 2, 4, 6, 8 etc. The third guard turns every third key ie 3, 6, 9, 12 etc and the fourth comes and does 4, 8, 12, 16 etc all the way up to the 100th guard who just turns the lock in 100. Then all the guards go to bed. How many prisoners can now escape?

10. The 'My Eye' Millennium Wheel has 10 cars equally spaced around the rim. In time for Maths Year 2000 the Department of Education wants the cars to be numbered from 1 to 10 inclusive. They want it done in a special way so that when you add up the numbers on any 2 cars next to each other, you get the same answer as if you added up the two numbers on the corresponding two cars on the diametrically opposite side of the wheel. Suggest a plan

There are lots of solutions - Can you see how many?