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Programming Enigma Puzzles

29 August 2018

Posted by on **From The Sunday Times, 12th September 2010** [link]

George has placed two vertical mirrors touching each other, with an angle between them. He has also placed a small cube between the mirrors and counted how many images there are of it in the mirrors. (For example, if the mirrors had 90 degrees between them, there would be three images). He wrote down two whole numbers – the angle between the mirrors, in degrees, and the number of images of the cube. When Martha saw the two numbers, she commented that their product, appropriately, was a perfect cube.

What was the angle between the mirrors?

**Note:** After much discussion of this puzzle, regular solvers of *The Sunday Times Teaser* puzzles have decided that the puzzle is flawed, and there is not enough information given to arrive at a unique solution. Nevertheless the puzzle has some interesting aspects to it.

[teaser2503]

14 February 2016

Posted by on **From The Sunday Times, 31st January 2016** [link]

I think of a whole number from 1 to 20 inclusive and Andy has to try to guess the number. He starts with three lives and makes successive guesses: after each guess I tell him whether it is right or too low or too high. If it is too high he loses one of his lives. To win the game he has to guess my number before his lives run out. He has developed the best possible strategy and can always win with a certain number of guesses or fewer. In fact no-one could be sure of winning with fewer guesses than that “certain number”.

What is that “certain number”?

[teaser2784]

15 November 2015

Posted by on **From The Sunday Times, 15th November 2015** [link]

King Lear III had a square kingdom divided into sixteen equal-sized smaller square plots, numbered in the usual way. He decided to keep a realm for himself and share the rest into equal realms (larger than his) for his daughters, a “realm” being a collection of one or more connected plots. He chose a suitable realm for himself and one for his eldest daughter and he noticed that, in each case, multiplying together [the] plot numbers within the realm gave a perfect square. Then he found that there was only one way to divide the remainder of the kingdom into suitable realms.

What are the plot numbers of the eldest daughter’s realm and of the king’s realm.

The puzzle text on The Sunday Times website, uses “any” where I have placed “[the]”.

[teaser2773]

14 August 2015

Posted by on **From The Sunday Times, 9th August 2015** [link]

King Lear II had a square kingdom divided into 16 equal smaller squares. He kept one square and divided the rest equally among his daughters, giving each one an identically-shaped connected piece. If you knew whether Lear kept a corner square, an edge square or a middle square, then you could work out how many daughters he had.

The squares were numbered 1 to 16 in the usual way. The numbers of Cordelia’s squares added up to a perfect square. If you now knew that total you could work out the number of Lear’s square.

What number square did Lear keep for himself and what were the numbers of Cordelia’s squares?

[teaser2759]

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