The problem of a disc supported on two pegs and disturbed by a horizontal force has been recently discussed by Griffin, Skelsey and Scorer (1965) mainly in terms of limiting equilibrium. However the way in which limiting equilibrium is approached, and breaks down through a transitional slipping at one peg, can be discussed within the simple laws of friction, provided only that we assume the peg supports are not perfectly rigid and obey some law of elasticity in providing a reaction opposite to their displacement. In the case when the pegs are far enough apart for the disc to be jammed between them, the reactions at the pegs may be indefinitely large, limited only by the breaking strength of the pegs or the possibility that the pegs may be forced so far apart as to allow the disc to pass between them. If the horizontal force on the disc is increased, equilibrium is then broken by slipping at one of the pegs, which is unrestrained and explosive. The cases of small and large friction coefficient are indistinguishable as limiting equilibrium states, because the disc is performing accelerated rotation about the other peg when either the pressure on the first peg becomes zero or slipping starts at the second peg. Thus in the case θ>λ>90θ – 2θ considered by Miss Griffin the limiting equilibrium state considered is not always attainable. Also the case quoted by Miss Skelsey under diagram 15 wherein equilibrium is never broken is physically impossible unless one of the pegs has a negative elastic constant or some additional mechanism is provided to increase the pressure between the pegs as the disturbing force is increased.

Everybody is familiar with the game of “Snakes and Ladders”, but not so many realise that the game constitutes an interesting example of a Markov chain. We feel that a good way of introducing Markov chain theory is by solving the problem, How long does a game of Snakes and Ladders last? Doubtless the reader has found that the last game before sending a child to bed seems to drag on interminably, and we used a computer to determine the actual average number of moves when 2 people play on a typical board.

Space does not allow much room for “reporting” in The Mathematical Gazette, though that deficiency is greatly offset by the Newsletter. As it happens, however, two very contrasting items arrived while this Number was in the proof stage and so they are included, as typical of much else, to give some information about mathematical activities in general.

This is the most ambitious attempt yet made to help mathematics teachers and pupils through the medium of television. It is designed for all but the least able pupils in the first year of the secondary school (i.e. of about 11 years of age), and will extend for two years. It aims to act as a guide-line for teachers who feel they would like to modernise their mathematics teaching both in content and method.