- Wethersfield c of e primary school

**Maths Challenges:**

**1. Mystery Matrix**

Have a look at this table square or matrix:

It is a little bit like our times tables grids.

Can you see how it has been constructed? For example..Why is there a 45 in the bottom right-hand corner?

You will notice that the numbers 2 to 9 are used to generate the matrix and only one of these numbers is used twice (2)

Can you fill in the matrix (table square) below?

The numbers 2 to 12 were used to generate it with, again, just one number used twice.

Can you create your own grid with missing numbers for a member of your family to complete?

__2. __**Peaches Today, Peaches Tomorrow...**

**(i)** A little monkey had 60 peaches.

On the **first** day he decided to keep 3/4 of his peaches.

He gave the rest away. Then he ate one.

On the **second** day he decided to keep 7/11 of his peaches.

He gave the rest away. Then he ate one.

On the **third** day he decided to keep 5/9 of his peaches.

He gave the rest away. Then he ate one.

On the **fourth** day he decided to keep 2/7 of his peaches.

He gave the rest away. Then he ate one.

On the **fifth** day he decided to keep 2/3 of his peaches.

He gave the rest away. Then he ate one.

**How many did he have left at the end?**

**(ii)** A little monkey had 75 peaches.

Each day, he kept a fraction of his peaches, gave the rest away, and then ate one.

These are the fractions he decided to **keep: **

1/2 1/4 3/4 3/5 5/6 11/15

**In which order did he use the fractions so that he was left with just one peach at the end?**

**(iii)** Whenever the monkey has some peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one.

I wonder how long he could make his peaches last for...

Here are his rules:

- Each fraction must be in its simplest form and must be less than 1.
- The denominator can never be the same as the number of peaches left.

For example, if there were 45 peaches left, he could not choose to keep 44/45 of them.

**Can you start with fewer than 100 peaches and choose fractions so that there is at least one peach left after a week?**

**Starting with fewer than 100, what is the longest you can make the peaches last?**

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