I love mathematical puzzles and, judging by the reaction I get when I try them out on classes, so do mathematics students. Here are three, all different in nature. Try and solve them first before looking on to the answers at the end.
The first one is geometrical:
A right-angled triangle is drawn in a circle with vertices on two radii, and on the circumference. Given that the circle has radius 6cm, how long is the hypotenuse of the triangle?
The next one is a matter of sorting out exactly what the words mean – and the more you try to solve it, the more brain-ache you get! No guessing – you must be able to justify your answer.
Mary is 36. She is twice as old as her husband was when she was as old as he is now. How old is her husband?
One of my favourites, simply because the answer seems so unlikely, is this one:
If you tie a piece of string around the Earth’s equator it will be approximately 40,000km, or 40 million metres, long. How much more string would you need for it to be lifted 1m above the equator, all the way round?
PUZZLE 1: Concentrating on the triangle can blind you to the fact that you can consider the shape in the circle as a rectangle with one diagonal drawn in. Draw in the other diagonal, and this will be a radius; both diagonals are the same length, so our line must be the same as the circle radius – 6cm.
PUZZLE 2: 27. When Mary “was as old as her husband is now” (27) it must have been 9 years ago, so he was 18. So she is twice as old as he was then.
PUZZLE 3: Have a guess – and ask other people to guess. Most people think it will be several kilometres at least. Let’s work it out: using the formula for the first piece of string, and working in metres:
The radius now needs to be increased by 1, so the new circumference will be:
In other words, the extra is or just over 6m!
Let me finish with one which is not strictly mathematical, but logical:
A man is looking at a portrait on the wall. He says: “Brothers and sisters have I none, but that man’s father is my father’s son.” Who is the man in the portrait?
Clue: Who is “my father’s son”? Answer will be in my next blog.