Upsetting Pitagoras

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

Triangle Mid Points

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

There and Back

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

Weekly Problem 15 - 2006

Stage: 4 Challenge Level:

The ratio width : height of television screens is changing from the traditional $4:3$ to the widescreen $16:9$.

If a traditional screen and a widescreen have the same area,
then what is the ratio widescreen width : traditional width ?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

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