Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
A hexagon, with sides alternately a and b units in length, is
inscribed in a circle. How big is the radius of the circle?
Triangle ABC has equilateral triangles drawn on its edges. Points
P, Q and R are the centres of the equilateral triangles. What can
you prove about the triangle PQR?
Evaluate these powers of 67. What do you notice? Can you convince
someone what the answer would be to (a million sixes followed by a
Equal touching circles have centres on a line. From a point of this
line on a circle, a tangent is drawn to the farthest circle. Find
the lengths of chords where the line cuts the other circles.
In a right-angled tetrahedron prove that the sum of the squares of
the areas of the 3 faces in mutually perpendicular planes equals
the square of the area of the sloping face. A generalisation. . . .
Alex and Tom have made good use of visualisations and their algebra
to solve this problem
Go to last month's problems to see more solutions.
You need to find the values of the stars before you can apply normal Sudoku rules.