Did you solve it? The enduring appeal of Venn diagrams

Venn diagram Photograph: Alex Bellos/alex bellos

Earlier today I set you these four Venn diagram teasers:

1) For each of the regions marked A to D below, think of a fraction that could belong in it, or say that it is impossible. (Each circle represents the set of fractions described by its rule.)

Solution

The question only asked for a single example for A to D. Here is a possible solution, but there are infinitely more.

2) For each of the regions marked A to H below, think of a number that could belong in it, or say that it is impossible. (A factor of a number is a number that divides into that number with no remainder.)

Solution

Again, here is just one possible solution.

One possible solution. Photograph: alex bellos

3) For each of the regions marked A to H below, think of five numbers that could belong in it, or say that it is impossible. (The mean is the sum of the numbers divided by 5, the median is the middle number when listed in order of size, the mode is the most common number and the range is the difference between the highest and the lowest number.)

Solution

Here’s one solution. I am assuming that if all the numbers are different, then all of the numbers are modes. (I haven’t had it checked, so if you spot a mistake please let me know!)

4. Draw a four set Venn diagram. The diagram needs to include four sets and all possible regions shared between the sets, i.e. there is a region in any one set, and outside all others; there is a region in any two sets and outside the others; there is a region in any three sets and outside the other; there is a region inside all sets.

Again, there are many ways to do this. The most common way is to use ellipses, as used by Crispian Jago in his Venn of irrational nonsense.

(6/6) Number 1: The Venn Diagram of Irrational Nonsense (464K Views)https://t.co/dfQzyCdpkV pic.twitter.com/6h1nE6xi56

— Crispian Jago #FBPE (@Crispian_Jago) November 7, 2018

Thanks to everyone who sent me their Venns. I liked this one best:

https://t.co/a6JUMCwcKw pic.twitter.com/RGhpModmk2

— Alex Turner (@Alexjturner) July 29, 2019

Thanks again to Craig Barton, who devised the first three puzzles. His website Maths Venns contains many similar problems. You can also find a huge amount of free material for teachers and students at Mr Barton Maths. He also has a podcast, and has written a critically-acclaimed book How I Wish I’d Taught Maths.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.