An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
The Queen of Hearts has lost her tarts! She is sure that those knaves who have not eaten the tarts will tell her the truth and the guilty knave will tell lies. When questioned the five knaves declare:
One of us ate them
Two of us ate them
Three of us ate them
Four of us ate them
Five of us ate them
How many of the knaves were honest?
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.