Prize Puzzle Competition 24

Closing date is 30th August 2000

70.

I have a 2-digit number. If the order of the digits is changed, it makes a new number which is 1 less than one-half of my number.

What is my number?

71.

A combination lock on a safe needs a 6-letter sequence to open the safe. This is made from the letters
A, B, C, D, E, F

with none of them being used twice.

Here are three guesses at the combination
C B A D F E A E D C B F E D F A C B In the FIRST guess only ONE letter is in its correct place.
In the SECOND guess only TWO letters are in their correct places.
In the THIRD guess only THREE letters are in their correct places.
Each of the 6 letters is in its correct place once.

What is the correct combination?

72.

A chess-board is made up of 64 black and white squares in the normal way, each having an edge length of 5 centimetres.
On this board the largest possible circle is drawn whose circumference lies completely in the white squares.

What is the radius of the circle?

The winner of Competition #23 was C. Dickinson of Middlesbrough.
The answers were:

67.	-40°F = -40°C
68.	23 different paths.
69.	Sqrt(46.25) or 6.8 metres (to 1 dec.place)