# Starter of the Week 16: Stairway to Heaven

Starting with the numbers: 2,4,6,8 fill in the bottom grid in any order. Work out the box above by adding the two numbers below.

Here are some possible questions to explore:

- What is the biggest possible total you can make in the top row?
- Create a hypothesis for a strategy that always gives the biggest possible total.
- Prove your result by considering integer numbers π, π, π, π
- When the ladder is now 5 blocks high, what is the biggest possible total for the numbers 2,4,6,8,10?
- Using letters π, π, π, π, π explain how you know you have found the largest total.
- Explore different heights of ladders. What is the pattern that would help you predict in terms of π, π, π, π … a ladder 8 blocks high?

**Teacher notes:**

Level of difficulty: Accessible for all students

Syllabus knowledge required: None β but would fit well with a lesson just before or just after introducing the binomial expansion and Pascalβs triangle.

You can download the pdf of the problem and the solution here.