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
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
A magical island is inhabited entirely by knights (who always tell the truth) and knaves (who always tell lies). One day 25 of the islanders were standing in a queue. The first person in the queue said that everybody behind was a knave. Each of the others in the queue said that the person immediately in front of them in the queue was a knave.
How many knights were there in the queue?
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.