Prize Puzzle Competition 9

25.The diagram is of an irregular pentagon with all 5 of its diagonals drawn in.

How many distinct triangles (not necessarily different) can be found, using only the lines (or parts of lines) in the diagram?


26.Alexis, Phil, Kit and Terri had a race.
Their finishing order was 1, 2, 3, 4 with no ties.
Phil beat Terri, but was not 1st or 3rd
Alexis was just one place in front of Terri.
What was their finishing order?

27.semicircle + rect. It is planned to make a flower bed in the shape
of a rectangle with a semi-circle attached at one edge.
It will have a perimeter of 10 metres.

What is the maximum area it could have?

The winner of Competition #8 was Matthew McDonald of Braunton, N. Devon.
The answers were:

22.55 or 99
23.1 minute to 10 (or 9:59)
24. 21 cm wide.
#22 was done correctly by nearly all entrants. Many gave both answers.
#23 was answered correctly by the majority of those who attempted it,
but there were several who gave the answer 1 minute past 10.
#24 was the difficult one. It was clear, from those who explained how they arrived at the answer,
that the question was not properly understood. Only a small minority got the correct answer.