Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves. . . .
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being
visible at any one time. Is it possible to reorganise these cubes
so that by dipping the large cube into a pot of paint three times
you. . . .
Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .
Sketch the graphs of y = sin x and y = tan x and some straight
lines. Prove some inequalities.
Draw the graph of a continuous increasing function in the first
quadrant and horizontal and vertical lines through two points. The
areas in your sketch lead to a useful formula for finding
Here the diagram says it all. Can you find the diagram?
Angus gives a very good account of how matrices, probability and graph theory are used in his solution.
Go to last month's problems to see more solutions.
This article introduces complex numbers, brings together into one
bigger 'picture' some closely related elementary ideas like vectors
and the exponential and trigonometric functions and their
derivatives and proves that e^(i pi)= -1.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.