### 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.

After $500$ games, I have won $500 \times \frac{49}{100} = 245$ games. So I have lost $255$ games. Therefore I need to win the next $10$ games to have a $50\%$ success rate.