### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### 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?

# Open the Box

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

A square piece of card has a square of side $2$ cm cut out from each of its corners. The remaining card is then folded along the dotted lines shown to form an open box whose total internal surface area is $180$ cm$^2$.

What is the volume of the open box in cm$^3$?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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