Belated gold stars to @chrishazell72 and @notonlyahatrack for the puzzle before last; no gold stars for the last one, a solution to which is here.
Dave's puzzle: Langford notices that the pair of yellow bricks are separated by one block, the pair of blue bricks separated by two blocks, and the pair of red bricks are separated by three blocks. How can you do the same thing with 4 or 7? Prove it's only possible for $n=4k - \frac 12 \pm \frac 12$.
Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008.
He lives with an espresso pot and nothing to prove.