Month: June 2024

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.

1. A = Odd numbers, B = Multiples of 4
2. A = Even numbers C= Prime numbers
3. A= Even numbers B=Multiples of 4

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:

https://brilliant.org/courses/infinity/

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