# Your Solutions - Stage 4 & 5

### Tens

##### Stage: 5 Challenge Level:

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

### Giants

##### Stage: 5 Challenge Level:

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?

### Squares from Diagonals

##### Stage: 3 and 4

Take a look at the video showing squares and their diagonals...

### Drawing Rhombuses

##### Stage: 3 and 4

Take a look at the video showing rhombuses drawn on dotty grids...

### Areas of Squares

##### Stage: 3 and 4

Take a look at the video showing areas of squares on a dotty grid...

### Areas on a Grid

##### Stage: 3 and 4

Take a look at the video showing areas of different shapes on dotty grids...

### Creating Squares - Game

##### Stage: 3 and 4

Play the game to create squares. Can you find a strategy?

### Coordinates of Corners

##### Stage: 3 and 4

Use the applet to make some squares. What patterns do you notice in the coordinates?

### Vectors Round a Square

##### Stage: 3 and 4

What is special about the relationships between vectors that define a square?

### Areas from Vectors

##### Stage: 3 and 4

Another solution was sent for the second question. No solutions for the last 2 questions.

### Find the Robber

##### Stage: 3 and 4

Play the game. How many guesses do you need to find the robber?

### Find the Metagiff

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

Play the game. How many guesses do you need to find the Metagiff?

### Going to the Cinema

##### Stage: 3 and 4

A cinema has 100 seats. Is it possible to fill every seat and take exactly £100?

### You Can't Make an Omelette...

##### Stage: 3 and 4

Can you devise the most efficient strategy for finding the highest floor from which you can drop an egg safely?

### Climbing the Stairs

##### Stage: 3 and 4

In how many ways can I get upstairs?

### Combining Lengths

##### Stage: 3 and 4

How many different lengths is it possible to measure with a set of three rods?