January 2014 Logic & Maths Puzzles
1. 
In many liquor stores you can buy pear brandy, with a real pear inside the bottle. The pear is whole and ripe, and the bottle is genuine; it hasn’t been cut in any way. How did the pear get inside the bottle?
2. 
The measuring cylinder on the left contains a litre of milk, the other a litre of water. Take one tablespoon of milk and mix it with the water. Now take one tablespoon of the water/milk mixture and mix it in with the pure milk to obtain a milk/water mixture. Is there:
A. more water in the milk/water mixture?
or
B. more milk in the water/milk mixture?
or
C. the same amount of water in the milk in the LHS cylinder as there is milk in the water in the RHS cylinder?
3. Draw the symbol that comes next in this sequence
4. Four Jolly men sat down to play
And played all night till break of day.
They played for cash and not for fun
With separate scores for everyone.
Yet when they came to square acounts,
They all had made quite fair amounts!
Can you this paradox explain?
If no-one lost, how could all gain?
5. 
The above diagram shows a green quarter-circle on which a brown rectangle has been superimposed. How long is the dark blue line?
6. Young Bill takes his dog Fido for a walk. He spots his best friend Fred exactly two kilometres away. Bill and Fred immediately start running toward each other at 10 km / hr each. At the same time, Fido slips his lead and runs directly toward Fred at 25 km /hr. As soon as he reaches Fred, he turns around and runs back to Bill. He then runs backward and forward between Bill and Fred until the two boys meet.
Assuming all travel is in straight lines and at constant speeds, how far will Fido have run between the time that the two boys see each other until they meet?
Hint: there are a number of difficult ways of working this out. There is an easy way.
7. 
The above net, consisting of orange, blue, red, yellow, pink and green squares can be folded to make a cubic box. Once assembled, which three pairs of colours will face opposite each other?
8. 
A steel washer with a hole in the middle is heated until the metal expands evenly by 1 percent. Will the hole in the washer get larger, smaller, or remain the same size?
9. A darts player scored 91 with a treble, a double and a single (no bulls).Given that the three numbers that he hits add up to 47 and that the difference between the largest and smallest of these three numbers is 5, how was this score made up?
10.
A necklace is made up of five identical red beads and two identical green beads on a ring. The ring is free to rotate, and the beads are free to slip around on the ring.
How many DIFFERENT such necklaces can be made using just five red beads and two green beads?