I haven’t yet looked at the comments about the puzzle I reported this morning that had been proposed by Russian Prime Minister Mikhail Mishustin when visiting a science-oriented “sixth form” class.
Here’s the puzzle again:
Construct a perpendicular from the (red) point on the circle to the diameter, without using any measuring devices.
In other words, given a circle with a diameter marked on it, and a point on the circle, can you find a way to draw a line from the point that hits the diameter at a right angle. (As marked in green above.)
The beauty of this question is the seemingly outrageous restriction not to allow measuring devices, which means that you cannot use a compass or a marked ruler. All you are allowed is an unmarked ruler to draw straight lines.
The Guardian has now published the four-step solution (there may be others); go to the preceding link to see it. Below you can see the PM drawing the solution (he must know his math).