Why 24?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Why 24? printable sheet



This problem is in two parts. The first part provides some building blocks which will help you to solve the final challenge. These can be attempted in any order. Of course, you are welcome to go straight to the Final Challenge without looking at the building blocks!

Click to reveal any of the questions below to get started.

Question A

Choose any whole number.

What happens when you multiply the numbers either side of it?

For example, if you choose $7$, work out $6 \times 8$. Repeat several times.

Notice anything interesting? Convince yourself it always happens.

Question B

Write down three consecutive numbers, none of which is a multiple of $3$. If you can't, explain why.

Question C

Choose two factors of $120$ which are coprime (they have a highest common factor of $1$).

Multiply them together and record the result. Repeat several times.

Notice anything about your results?

Start with numbers other than $120$. Does the same thing always happen? Convince yourself.

Question D

Choose any two consecutive even numbers.

Multiply them together and record the result. Repeat several times.

Notice anything interesting? Convince yourself it always happens.

 

FINAL CHALLENGE

Take any prime number greater than $3$, square it and subtract one. Repeat several times.

Notice anything interesting? Convince yourself it always happens.