| 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.
|