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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.

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Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

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Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Mini Kakuro

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

From the second row we see that c, d, e are 1, 2, 4 in some order; and from the third column we see that e> 2. Hence e=4 and we may now deduce that g=8 and so f=5.

(Although their values are not required, it is now also possible to deduce that c=1, a=3, b=9, d=2.)

This problem is taken from the UKMT Mathematical Challenges.

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