# May 2002, All Stages

## Problems

### Chain of Changes

##### Stage: 1 Challenge Level:

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

### What Are You Plotting?

##### Stage: 2 Challenge Level:

Investigate the positions of points which have particular x and y coordinates. What do you notice?

### Treasure Island

##### Stage: 2 Challenge Level:

Write down what you can see at the coordinates of the treasure island map. The words can be used in a special way to find the buried treasure. Can you work out where it is?

### A Cartesian Puzzle

##### Stage: 2 Challenge Level:

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

### The Lily Pond

##### Stage: 2 Challenge Level:

Freddie Frog visits as many of the leaves as he can on the way to see Sammy Snail but only visits each lily leaf once. Which is the best way for him to go?

### World of Tan 28 - Concentrating on Coordinates

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

### Coordinate Tan

##### Stage: 2 Challenge Level:

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

### Teddy Town

##### Stage: 1, 2 and 3 Challenge Level:

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

### Plate Spotting

##### Stage: 2 Challenge Level:

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

### Transformation Tease

##### Stage: 2 Challenge Level:

What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?

### Red Even

##### Stage: 2 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

### Going Loopy

##### Stage: 3 Challenge Level:

Draw some spirals with the LOGO programming language.

##### Stage: 3 Challenge Level:

Is it possible to use all 28 dominoes arranging them in squares of four? What patterns can you see in the solution(s)?

### Powerful Factorial

##### Stage: 3 Challenge Level:

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

### Similarly So

##### Stage: 4 Challenge Level:

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

### Approximating Pi

##### Stage: 4 and 5 Challenge Level:

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

### Double Angle Triples

##### Stage: 5 Challenge Level:

Try out this geometry problem involving trigonometry and number theory

### 30-60-90 Polypuzzle

##### Stage: 5 Challenge Level:

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

### Remainder Hunt

##### Stage: 5 Challenge Level:

What are the possible remainders when the 100-th power of an integer is divided by 125?

### Binary Squares

##### Stage: 5 Challenge Level:

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?