Earlier today I set you these four Venn diagram teasers:
1) Think of a fraction that could belong in each of the regions marked A to D below, 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) Think of a number that could belong in each of the regions marked A to H below, 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.
3) Think of 5 numbers that that could belong in each of the regions marked A to H below, 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.
Thanks to everyone who sent me their Venns. I liked this one best:
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.