## Problems

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

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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

Bluey-green, white and transparent squares with a few odd bits of
shapes around the perimeter. But, how many squares are there of
each type in the complete circle? Study the picture and make. . . .

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

Can you use LOGO to create a systematic reproduction of a basic
design? An introduction to variables in a familiar setting.

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

Learn how to use Excel to create triangular arrays.

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

Use Excel to investigate the effect of translations around a number
grid.

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

This spreadsheet highlights multiples of numbers up to 20 in
Pascal's triangle. What patterns can you see?

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

Use Excel to create some number pyramids. How are the numbers in the base line related to each other? Investigate using the spreadsheet.

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

Cut off three right angled isosceles triangles to produce a
pentagon. With two lines, cut the pentagon into three parts which
can be rearranged into another square.

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

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

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

Can you show that you can share a square pizza equally between two
people by cutting it four times using vertical, horizontal and
diagonal cuts through any point inside the square?

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

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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