We looked at Math Pickle’s brilliant activity. Finishing up with working out this probability:
![](https://lycee.samicharity.co.uk/wp-content/uploads/2024/06/image-6-1024x317.png)
We looked at Math Pickle’s brilliant activity. Finishing up with working out this probability:
This activity was inspired by this numberphile video by Neil Sloane.
Here are the only distinct three ways you can draw two circles in a Venn diagram.
If we take the universal set to be the positive integers, we can come up with some sets that would fit for A and B for the three examples.
Note that these choices mean that there is at least one number in each region.
Now for the challenge …
Draw all the different Venn diagrams you can make with three circles, and find rules for them all.
Number of ways can be found here. A picture of them all is here.
Watch the numberphile video to find out how many Jonathan Wild found for 4 and 5 circles. It is a lot more! Nobody knows for 6 …
We spent today learning about infinity and Hilbert’s Infinite Hotel:
You might be familiar with divisibility rules such as “A number is divisible by 3 if the sum of the digits is divisible by 3”. You can see some more here.
Our investigation today was – can we develop a set of divisibility rules for binary numbers?
Divisible by 2
This was straightforward. If the rightmost (unit) digit is 0 then the number is divisible by 2.
e.g. The number 6 is divisible by 2
but the number 7 is not
Can you extend this logic to create a divisibility rule for powers of 2 (e.g. 4, 8, 16 …)? Solution