Christmas Puzzles

At my job, my department (some guy called Aiden) sent out some Christmas puzzles to work through.

--------------------*******Christmas Puzzles********--------------------
100 Coins:
You have 100 coins. 10 are heads. 90 are tails. you cannot look/feel to see which way up the coins are. How do you divide them into two piles, each with the same number of heads showing in them?

Truck Travel:
You have 5 trucks. Each truck has a tank of 100 litres of fuel. it also has  a spare tank of 100 litres. A truck can do 10 miles on a litre of fuel.

You need to transport someone along a road just using the trucks. Fuel can be transferred at will between the trucks. How far can you get? How do you do it?

How many times in a day do an analogue clock's hands overlap?


I’ve had a play around, and my answers to the puzzles are as follows:

  • 100 coins: take 10 coins from the 100-coin-pile, flip those 10 coins, and then set them as the new pile. Each pile has the same number of heads.

  • Truck Travel: If the 5 trucks each start wtih 100L of fuel, then the person can be transported 3333 miles. If the 5 trucks each start with 200L of fuel, then the person can be transported 4566.6 recurring miles.

  • Clocks: An analogue clock's hands overlap 22 times in a day.

I have no idea if these are the right answers, I look forward to talking about them with my work pals when I get back.

You can see my workings in the following blogs:

Coin Puzzle

Truck Puzzle

Clock Puzzle