# Prize Puzzle Competition 8

 22 Take the 2-digit number 45.Square it (45 x 45) to make 2025Split this 4-digit number in half to make 20 and 25Add them (20 + 25) to make 45Which 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 beOdd numbers + 5Even numbers + 6=> ELEVEN for 16p 20 Identify the containers as  and One way of doing it is to -Fill  and pour that into .Fill  and pour as much as possible into .This will leave 1 litre in Empty Pour the 1 litre from  into Fill  and pour that into .There will then be 4 litres in .There are other ways. 21 Euler's Law for solids states that number ofFaces + Vertices - Edges = 2In this case there are 9 vertices so, F + 9 - E = 2If 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 = 2f = 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?