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Trig Rules OK
Age 16 to 18
Challenge Level 
The problem suggests a property shared by the triangles which
always holds no matter how the squares are changed. The challenge
is to make and prove a conjecture about this property.
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Polite Numbers
A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?
Least of All
A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.