# Sets and Groups - March 2005, Stage 3&4

## Problems

### Consecutive Seven

##### Age 11 to 14 Challenge Level:

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

### Shuffle Shriek

##### Age 11 to 14 Challenge Level:

Can you find all the 4-ball shuffles?

### Stars

##### Age 11 to 14 Challenge Level:

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

### Arithmagons

##### Age 14 to 16 Challenge Level:

Can you find the values at the vertices when you know the values on the edges?

### Spot the Card

##### Age 14 to 16 Challenge Level:

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

### Sheffuls

##### Age 14 to 16 Challenge Level:

Discover a handy way to describe reorderings and solve our anagram in the process.