### 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.

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?

### 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...

# Weekly Problem 30 - 2015

##### Stage: 3 and 4 Challenge Level:

Consider the following table:

The numbers in the first column are fixed and $a$, $b$, $c$ and $d$ should be chosen so that in the entire table the total number of $1$s is $a$, the total number of $2$s is $b$, the total number of $3$s is $c$ and the total number of $4$s is $d$.

Here is an example:

In the entire table there are two $1$s, three $2$s, two $3$s and one $4$.

How many other ways can you find to fill in the right-hand column? Can you find them and explain why there are no others?

This problem is taken from the UKMT Mathematical Challenges.

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