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Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Contact

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

Ratio Sudoku 2

Age 11 to 16 Challenge Level:

Caitlin kept a record of the order in which she filled the Sudoku.

She filled the cell marked 1 first, then the cell marked 2, then the cell marked 3...

You might like to retrace her route to fill in the cells in the same order, though this is just one possible route through the problem.

You can print her journey here.