2 out of 3
How much of the field can the animals graze?
3 out of 3
To avoid losing think of another very well known game where the patterns of play are similar.
3 out of 3
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
3 out of 3
3 out of 3
Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.
3 out of 3
Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?
3 out of 3
The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
3 out of 3
Can you use the diagram to prove the AM-GM inequality?
3 out of 3
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
