|85.||A 4 by 4 grid, like that shown, is to be cut into 4 pieces. Cutting may only be done along the lines and the 4 pieces must be identical to each other in both size and shape.|
To see if pieces match each other they may be turned around but not turned over.
In how many different ways can this be done?
|86.||My office is on the 3rd floor and, though there is a lift, I like using the big circular staircase. I go up the stairs 2 at a time (to get more exercise) but am annoyed that there is always just 1 stair left over when I get to my landing.|
One day, in a burst of energy I went up the stairs 3 at a time, and still had 1 stair left over!
By counting (certainly not by doing it!) I established that even if I could go up 4, 5 or 6 stairs at a time there would still be 1 left over.
Worse yet, no matter how many stairs I did at a time (except for 1 or the lot) there would always be some left over.
How many stairs are there to my office?
|87.||A new recreation space is being laid out. It will be oblong in shape and 55 metres long, but no width has yet been fixed.|
A square swimming-pool is to be placed in the middle of the length, and is to fill the full width of the space, leaving a paved area at each end.
To get the largest possible paved area,
what should be the width of the recreation space?
The winner of Competition #28 was Steve Morris of Sandbach, Cheshire.
The answers were:
|82.||The digit 1 appears 301 times.|
|83.|| The start must be at B or F and the finish at F or B.|
There are many possibilities, but each letter must appear twice.
|84.||n = 664 gives 2086 (+0.0175 . . .)|