### 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.

### 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?

### 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...

# Rolling Along the Trail

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

A pair of dice is thrown and the score is obtained by finding the product of the two numbers on top of the dice when they land.

In five throws of both dice:

the second score is $5$ more that the first;
the third score is $6$ less than the scond;
the fourth score is $11$ more than the third;
the fifth score is $8$ less than the fourth.

What was the score for each of these five throws?

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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