Prize Puzzle Competition 23

Closing date is 30th June 2000

67. The two main scales used for measuring temperature are the Fahrenheit and the Celsius scales.
Some commonly-used temperatures are shown on the right as they would be shown on those scales.
You might notice that they seem to get closer together as they go down.

At what temperature do both scales read the same?
Fahrenheit Celsius
Boiling point
of water is
Blood heat is98.6°F 37°C
Freezing point
of water is

68. Puzzle Maze The drawing on the left is a simple puzzle-maze through which you have to find a path from IN to OUT.
Did you notice that different paths are possible?
With the restriction that no passage may be used more than once in any path,

how many different paths are possible?

69. A room is 3 metres high by 4 metres wide by 5 metres long.
In the middle of one of the end (smaller) walls is a male spider.
In the topmost corner of the opposite end wall is a female spider.
The male wishes to get better acquainted with the female.

What is the length of the shortest distance he must scuttle to do that?

The winner of Competition #22 was Julia Jasper of Carmel RC Tech. College, Darlington.
The answers were:

64.  The smallest Harshad number divisible by 13 is 247
65.  B + D = 10
66.  1000/pi [or 318.3 metres]