# Thinking Systematically - October 2003, Stage 2&3

## Problems

##### Age 7 to 11 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.

##### Age 7 to 11 Challenge Level:

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

##### Age 7 to 11 Challenge Level:

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

##### Age 7 to 11 Challenge Level:

A group activity using visualisation of squares and triangles.

##### Age 7 to 11 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?

##### Age 7 to 11 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?

##### Age 7 to 11 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.

##### Age 7 to 14 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.

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

How many different symmetrical shapes can you make by shading triangles or squares?

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

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

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

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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

Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.

##### Age 11 to 16 Challenge Level:

Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
your logic?

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