Teaching mathematics has its rewards but there are moments when not even the money is adequate compensation. I once had an A level mathematics retake by the name of Achmed who turned up for a one-to-one tutorial with no textbook, no paper to write on, and no pen to write with. All he brought was himself. Since I was not required to bring any paper of my own there was clearly a need to improvise. So I visited the toilet next door, unravelled a few sheets of toilet paper from the roll (the tracing paper sort that makes sandpaper feel like comfort), and returned to the teaching room waving the sheets in triumph. And there I was for an hour, sketching a whole series of carefully labelled graphs on small rectangles of toilet paper to illustrate the concept of curve transformations. At the end of the session, smouldering with self-satisfaction at the clarity of my exposition, I proudly presented Achmed with the graphs expecting him to take them home and, with due respect, neatly insert them in his clip file. However, as he opened the door to leave, without a moment's thought, he casually screwed them up into a ball and hurled them in the bin! As King Lear aptly put it: "How sharper than a serpent's tooth it is to have a thankless child".

This incident, and his subsequent inability to produce any work of note over a nine-month period (Achmed not King Lear) convinced me that some students are simply beyond redemption, at least without repeated exposure to some first-rate therapy. I'm also convinced that Isaac Newton, had Achmed been around in 1685, would have thought again about the laws of mechanics in his Principia and revised his first law of motion to read: "An Achmed at rest, remains at rest unless, or even if, acted on by an external force." Unfortunately, the only thing that enthused Achmed was Budweiser and lots of it!

Graph plotting, I tell my students, is where mathematics and art meet. Armed with a keen eye and a sharp pencil, it demands the connection of crossing coordinates and the coordination to connect crosses. I've seen graphs drawn with an unsharpened HB pencil with a point so thick that the result might easily have impressed van Gogh. With a pencil curve half a centimeter wide, plotted points become lost in a mist of charcoal, rather like Achmed who seemed to have missed the point when he once asked if it were possible to draw a graph in four dimensions. I assured him that even after ten pints of Budweiser and the attendant double vision he would still be incapable of visualising it. I suspect poor Achmed would even have struggled to visualise the two-dimensional graph shape below which was taken from a Core 3 mathematics A level paper and serves as the subject of this week's puzzle.

What capital letter should be placed to the right of the lower left point of the graph (shown)?

To solve The Traffic Lights Puzzle, each colour must be written out as follows: GREEN, RED, YELLOW and the number below it gives the position of the letter in that colour that must be used. So the first letter of GREEN is G, the second letter of RED is E, and the third letter of YELLOW is L which makes the word GEL.