Some mathematicians say that mathematics is the science of patterns. Here we invite you to explore some situations and notice the patterns that emerge, before going on to explain and perhaps prove them.

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. Try it a few times - notice anything?

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number? Explore this and other related questions, and see if you can prove your findings.