Prize Puzzle Competition 8

22.Take the 2-digit number 45.
Square it (45 x 45) to make 2025
Split this 4-digit number in half to make 20 and 25
Add them (20 + 25) to make 45
Which is what you started with.
Find another 2-digit number which does the same.

23.A group of four people, when asked the time gave these different answers -
Jan said said it was "3 minutes past10"
Kit said said it was "3 minutes to10"
Nicky said said it was "6 minutes to10"
Terri said said it was "2 minutes past10"
They were all supposed to be telling the same time!They were all wrong.
Their errors (in no particular order) were 2, 3, 4 and 5 minutes.
What was the correct time?

24.The drawing is of the flag of St. George.
It consists of a red cross on a white background.
Both arms of the red cross are the same width.
The flag measures 60 cm by 91 cm.
If the area of the red arms is equal to the area of white,
what should be the width of the red arms?

The winner of Competition #7 was Chris Nevett of Heathside School, Weybridge
The answers were:

19.The logic seemed to be
Odd numbers + 5
Even numbers + 6
=> ELEVEN for 16p
20.Identify the containers as [3] and [5]
One way of doing it is to -
Fill [3] and pour that into [5].
Fill [3] and pour as much as possible into [5].
This will leave 1 litre in [3]
Empty [5]
Pour the 1 litre from [3] into [5]
Fill [3] and pour that into [5].
There will then be 4 litres in [5].There are other ways.
21. Euler's Law for solids states that number of
Faces + Vertices - Edges = 2
In this case there are 9 vertices so, F + 9 - E = 2
If there are f faces then, there must be 3f /2 edges.
(Which means there must be an even number of faces)
So f + 9 - 3f /2 = 2
f = 14 => There are 14 faces.
#19 was done by many but, judged by the answers alone (since no reasons were asked for and were rarely given) a lot of guessing was being used.
#20 was done by nearly everyone and there were extremely few wrong answers.
#21 had a very small entry and most of those were wrong. Is the knowledge of topological matters so neglected?