This is a collection of some of my favourite puzzles. Many of these, I love because of the elegance and simplicity of their solution. Others have a cleverly crafted story around the puzzle. Still, others are intriguing because of their complexity. Whatever the reason, they’re all challenging. Enjoy!

## How did I get around?

I decide to cycle around the local park in an anticlockwise direction, but never once do I turn left. How did I do it?

Solution 1

Solution 2

This solution has fewer loops.

## Exactly half full

I have a cylindrical glass and an unlimited supply of water. How can I fill the glass exactly half full of water without the use of any measuring aids?

Solution

Fill the glass more than half full with water and then tip some water out until the water level touches the bottom and front lip of the glass as shown.

A cross-section of the centre reveals that we’re dealing with identical triangles.

When uprighted, the glass will be exactly half full of water.

## Where is the father?

A mother is 21 years older than her child. In exactly six years from now, the mother will be exactly five times as old as the child. Where is the father?

Solution

## A bottle and a cork

A bottle and cork cost $1.10. If the bottle costs a dollar more than the cork, how much does the cork cost?

Solution

## Exactly 4 litres

I have two cylindrical containers. One has a five-litre capacity; the other has a three-litre capacity. I have an unlimited supply of water. How can I get exactly four litres of water?

Solution 1 – The Die Hard 3 version

5L container (A) | 3L container (B) | Note | Generalised form |
---|---|---|---|

5 | 0 | Fill the 5L container from the tap. | |

2 | 3 | Empty the 5L container into the 3L container leaving 2L in the 5L container. | A-B in A |

2 | 0 | Empty the 3L container. | |

0 | 2 | Transfer the 2L of water across from the 5L container to the 3L container. | Space in B is B-(A-B) or 2B-A |

5 | 2 | Fill the 5L container from the tap. | |

4 | 3 | Top up the 3L container with 1L of water from the 5L container leaving 4L of water in the 5L container. | Amount in A is A-(2B-A) or 2(A-B) |

This solution is the least environmentally sustainable as it wastes 6L of water.

Solution 2 – A longer version

5L container (A) | 3L container (B) | Note | Generalised form |
---|---|---|---|

0 | 3 | Fill the 3L container from the tap. | |

3 | 0 | Transfer the contents of the 3L container across to the 5L container. | Space in A is A-B |

3 | 3 | Fill the 3L container from the tap. | |

5 | 1 | Top up the 5L container with 2L of water from the 3L container leaving 1L of water in the 3L container. | Amount in B is B-(A-B) or 2B-A |

0 | 1 | Empty the 5L container. | |

1 | 0 | Transfer the contents of the 3L container across to the 5L container. | |

1 | 3 | Fill the 3L container from the tap. | |

4 | 0 | Transfer the contents of the 3L container across to the 5L container leaving 4L of water in the 5L container. | Amount in A is B+(2B-A) or 3B-A |

This solution, while longer, is slightly more environmentally sustainable as it only wastes 5L of water.

Solution 3 – The quickest version

5L container (A) | 3L container (B) | Note | Generalised form |
---|---|---|---|

2.5+ | 1.5+ | Fill the 5L and 3L containers slightly more than half full. | |

2.5 | 1.5 | Tip some of the water out so that each container is exactly half full. See puzzle Exactly half full | Amount in A is A/2. Amount in B is B/2. |

4 | 0 | Transfer the contents of the 3L container across to the 5L container. | Amount in A is (A+B)/2 |

This is not only the quickest solution. It is also the most environmentally sustainable solution as it wastes very little water. This makes it a very efficient solution.

## Shortest path

I went camping with the family. We had pitched the tent not far from a riverbank at the spot marked B. My daughter had gone to fetch some water in a billy, but on the way got distracted and wandered off picking wildflowers at A. “Where’s the water?” I called out. “I can’t make tea without it!”. If my daughter is to take the shortest path from A to B via the riverbank, where on the riverbank would she fill the billly?

Hint!

The shortest distance between two points is a straight line.

Solution

Mirror point A on the opposite side of the riverbank so it appears at C. Draw a line between B and C. For the shortest path, where that intersects with the riverbank at D is where the water should be collected.