# Number - March 2007, All Stages

## Problems

### 100 Square Jigsaw

##### Stage: 1 Challenge Level:

Can you complete this jigsaw of the 100 square?

### Growing Garlic

##### Stage: 1 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

### Street Sequences

##### Stage: 1 and 2 Challenge Level:

Investigate what happens when you add house numbers along a street in different ways.

### Multiplication Square Jigsaw

##### Stage: 2 Challenge Level:

Can you complete this jigsaw of the multiplication square?

### Factor-multiple Chains

##### Stage: 2 Challenge Level:

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

### Multiples Grid

##### Stage: 2 Challenge Level:

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

### Triangle Numbers

##### Stage: 3 Challenge Level:

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

### Cunning Card Trick

##### Stage: 3 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works?

### Route to Infinity

##### Stage: 3 and 4 Challenge Level:

Can you describe this route to infinity? Where will the arrows take you next?

### Twizzles Venture Forth

##### Stage: 4 Challenge Level:

Where we follow twizzles to places that no number has been before.

### Twizzle Arithmetic

##### Stage: 4 Challenge Level:

Arrow arithmetic, but with a twist.

### Twizzle Wind Up

##### Stage: 4 Challenge Level:

A loopy exploration of z^2+1=0 (z squared plus one) with an eye on winding numbers. Try not to get dizzy!

### Twizzle Twists

##### Stage: 4 Challenge Level:

Make the twizzle twist on its spot and so work out the hidden link.

### Elevens

##### Stage: 5 Challenge Level:

Add powers of 3 and powers of 7 and get multiples of 11.

### Tens

##### Stage: 5 Challenge Level:

When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?

### Bina-ring

##### Stage: 5 Challenge Level:

Investigate powers of numbers of the form (1 + sqrt 2).