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Have You Got It?

Can you explain the strategy for winning this game with any target?

Counting Factors

Is there an efficient way to work out how many factors a large number has?

Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

Threesomes

Age 11 to 14 Challenge Level:

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

Can you draw triangles of area 1, 2, 3, ... square units?

Can you draw a triangle with an area of 1.5 square units?

What is the area of the smallest triangle you can draw? Is this triangle unique?

How many triangles of of area 2 square units can you draw and can you create "families" or "groups" of these triangles?