# April 2003, All Stages

## Problems

### Domino Sequences

##### Stage: 1 Challenge Level:

Find the next two dominoes in these sequences.

### Take the Right Angle

##### Stage: 2 Challenge Level:

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

### The Mathemagician's Seven Spells

##### Stage: 2 Challenge Level:

"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?

### Ten Green Bottles

##### Stage: 2 Challenge Level:

Do you know the rhyme about ten green bottles hanging on a wall? If the first bottle fell at ten past five and the others fell down at 5 minute intervals, what time would the last bottle fall down?

### Slow Coach

##### Stage: 2 Challenge Level:

How many of this company's coaches travelling in the opposite direction does the 10 am coach from Alphaton pass before reaching Betaville?

### Light Blue - Dark Blue

##### Stage: 2 Challenge Level:

Investigate the successive areas of light blue in these diagrams.

### Squares, Squares and More Squares

##### Stage: 3 Challenge Level:

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

### Sissa's Reward

##### Stage: 3 Challenge Level:

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

### Squaring the Circle and Circling the Square

##### Stage: 4 Challenge Level:

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

### The Root of the Problem

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

Find the sum of the series.

### Staircase

##### Stage: 5 Challenge Level:

Solving the equation x^3 = 3 is easy but what about solving equations with a 'staircase' of powers?