Prize Puzzle Competition 11

Closing date is 3rd July 1998

31. The drawing on the right is of a "puzzle dartboard".
Each dart scores the number written in the cell in which it lands.
You may throw as many darts as you like,
but must score exactly 100.
What is the least number of darts you would need,
and in which cells must they land?
160 24
039 0
230 17

32. A new monument is to be made in the shape of a cuboid.
Only three of the faces are to be decorated.
To allow for this:
one face has to have an area of 48 square metres;
another to have an area of 72 square metres;
and another of 96 square metres.
What will be the volume of the monument?

33. Jack set out on a walk at a steady 2 miles per hour.
Thirty minutes later, Jill set out to follow him, jogging at a steady 4 miles per hour.
Rascal, the dog, left at the same time as Jill and ran at 10 miles per hour, from Jill to Jack, then back to Jill, than back to Jack, and so on until Jill caught up with Jack.
How many miles had Rascal run by then?

The winner of Competition #10 was Henry Parkes of Langton Matravers.
The answers were:

28.(a) 37 (b) 55 and a half
29.Replace 9 with 17
30. 24 and 30 sq.metres. (6, 8, 10) and (5, 12, 13)
#28 answers were nearly all correct - a few failed to get the 'half' in part (b).
#29 was the hardest. Not many (correct) answers to this one.
#30 was generally well done, presumably helped by the fact that the required triangles were amongst the smallest in the Pythagorean series.