### 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.

### 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?

# Product and Sum

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

Jim rolled some dice and was surprised that the sum of the scores on the dice was equal to the product of the scores on the dice. One of the dice showed a score of $2$, one showed $3$ and one showed $5$. The rest showed a score of $1$. How many dice did Jim roll?

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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