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 11 - 2015

Stage: 3 and 4 Challenge Level:

The pages of a book are numbered $1$, $2$, $3$, $\dots$ In total, it takes $852$ digits to number all the pages of the book.

What is the number of the last page?

This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution
View the current weekly problem