# Thinking Systematically - October 2003, Stage 1&2

## Problems

### 1, 2, 3 Magic Square

##### Stage: 2 Challenge Level:

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

### A Square Deal

##### Stage: 2 Challenge Level:

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

### Seven Pots of Plants

##### Stage: 2 Challenge Level:

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

### Diagrams

##### Stage: 2 Challenge Level:

A group activity using visualisation of squares and triangles.

### Counters

##### Stage: 2 Challenge Level:

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

### Triangle Island

##### Stage: 2 Challenge Level:

You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?

### Symmetry Challenge

##### Stage: 2 Challenge Level:

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

### Make 37

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

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.