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
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
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?
3 out of 3
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
3 out of 3
What is the units digit of the given expression?
1 out of 3
How can you decide if a graph is traversable?
1 out of 3
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
2 out of 3
Can you tangle yourself up and reach any fraction?
