This week's puzzle concerns the inhabitants of Quiz Master Shop Towers and our route to the Jolly Quizmasters Arms for our evenings' libations.
To get to the road we have to cross a square field, entering through a gate at the south west corner and exiting through another gate halfway along the eastern edge.
Because we go at irregular times (we work long into the evenings on some days preparing top quality questions for our customers!) we have to go to the wall along the north edge to wave to our neighbours, so that they can join us for a tincture.
Our route is rather like the logo that accompanies this blog.
It doesn't matter where we are along the wall when we wave, as our neighbour can see all of it. Clearly, we want to take the shortest possible route across the field, to maximise our drinking before closing.
What is the shortest route?
Well, we should aim for a point on the wall one third of its length from the north east corner.
If you imagine another field the same size, on the north side of this one. That is, two identical fields touching along the wall in question. If the gate were halfway along the eastern side of the second field, the shortest route would be a straight line across the two fields, climbing over the wall.
From this you end up with two similar triangles; one with its base along the southern side of the first field, and the other with its base along the wall. The bigger triangle has a height of one and a half fields, and the smaller a height of half a field. The bigger triangle is three times as tall as the smaller triangle, and so the smaller triangle's base must be one third of the bigger triangle's base.