or eliminate d and solve,

]]>Here is my diagram for the others:

The boys numbers are in blue; girls in red; unknown in green.

Bob

]]>Sorry. I could not follow what you are asking. Life for me is too short to read and follow all of Euclid's elements. Problems with geometry I may be able to do, but getting inside his head is beyond me.

Bob

It's ok. The ideas still holds and it doesn't make it false it's just the way it is done which I found weird.

]]>Welcome to the forum.

Angle BAP = ADP ( see http://www.mathisfunforum.com/viewtopic.php?id=17799 post 7 )

The ratio result then follows from "triangles ABP and DAP are similar".

Bob

]]>To tell the truth, I cannot remember exactly what the questions were, just his answer to Q3. It'd be a shame to be unable to tell the story just because of that so I made up Q1 and Q2 both times. It was certainly a set of questions about symmetry and the third question definitely said to draw a picture. And that's the point: The book couldn't give a picture as an answer hence the 'Show your picture.....' answer. Also my memory isn't so great that I remember telling the story more than once. I might have told it three times. Now we have fully analysed the script hopefully you'll forgive me and we can move on.

math9maniac wrote:

Would you say the study for the degree was somewhat difficult?

Yes, but I enjoyed it. Up until that level, I can still remember and do the maths I was taught. But most of the university stuff has long since faded from my memory. If someone asks a question here about one of those topics I can sometimes do some research and remind myself, but some of it I never really understood properly. I did get asked to explain stuff by fellow students, so it seems the teaching aspect was beginning to kick in, even then.

When the government decided to give each school its first computer ( a research machine 380 Z ) the school had to have two teachers qualified to use it. Much to his amusement, my head of department was considered qualified as he had done a course ten years before (and forgotten most of it) but I was not. So I had to go to college to learn how to put a floppy disc in a machine to load up an operating system . As I could do stuff like that I was allowed to sit in the corner and write a program in BASIC.

Bob

]]>I have re-worked this and I agree completely with all your answers. No idea what went wrong before. Maybe I only had V or only A. I dislike questions that get you to condense answers like this. If you get one correct but not the other you get no marks instead of half marks. And no clues about what you did wrong. I think it's just a lazy way to use a computer to mark the answers rather than doing it properly.

Anyway, thanks for your contribution.

Bob

That's the second time this week. Oh dear! At least I'm getting them right now, so I can dismiss senility. You are not by any chance related to championmathsgirl are you?

]]>http://www.slimy.com/~steuard/teaching/ … range.html

It is usual to begin the study of anything with the simplest examples and problems possible.

I can provide simple but less exciting examples.

]]>http://www.mathsisfun.com/geometry/comp … ngles.html

So let us call the second angle b. From the definition we know that a + b = 90. Understand so far?

]]>13. Which of the following is accurate?

AThe inverse of the statement is "If someone is a baseball player then someone is an athlete."

BThe statement is "If someone is an athlete, then they are a baseball player."

CThe statement can never be true.

DBaseball players all have great teeth and gums.

E The inverse of the statement is not true.

F The converse is: "Joey is a baseball player, and he is not an athlete."

14. What is q?

ASomeone is an athlete.

BSomeone is a baseball player.

CAll baseball players are athletes.

DAll athletes are baseball players.

E Baseball player

F Athlete

25 students played soccer

4 boys played soccer and baseball

3 girls played soccer and baseball

10 boys played baseball

4 girls played baseball

9 students played tennis

3 boys played soccer and tennis

3 girls played soccer and tennis

3 boys played baseball and tennis

1 girl played baseball and tennis

1 boy played all three sports

1 girl played all three sports

Hints on the diagram (highlight the following paragraph with your mouse to see them):

<start highlighting here> Notice that the counts don't make sense as they are, because they're all inclusive. The soccer count includes every who plays soccer, even the students in the soccer and baseball, soccer and tennis, and the all three sport counts. The count for soccer and baseball includes the students who play all three sports. So you'll need to correct from the inside outward...first subtract the boy and girl who play all three sports from all the other counts, then subtract the dual-sport counts from the single sport counts.

Put another way, this is like the gecko problem--the entire soccer circle including the soccer and baseball students and the soccer and tennis students and the students who play soccer and baseball and tennis, will add up to 25.<end highlighting here>

18. How many students played soccer and baseball, but not tennis?

A5

B10

C3

D4

E 7

F 13

20. How many girls played only baseball?

A7

B2

C3

D4

E 10

F 1

Bob

]]>For 8 queens, according to Wikipedia, there are 12 fundamental solutions (rotations and reflections count as one solution only) and 92 distinct solutions (rotations and reflections create new solutions). What are the corresponding numbers for placing 32 knights? (You might also want to try rooks (apparently thousands), bishops and kings, but those are probably larger numbers).

Also, if we stick the two opposing edges of the chessboard together to make a cylinder (without bases), how many queens can we place at most on the board? (so that there still is no pair of attacking queens)

]]>Welcome to the forum.

This is known as a conditional probability problem. The correct result can catch you out.

Let's say the three white marbles can be told apart in some way. eg. We write 1, 2 and 3 on them. I'll refer to them as W1, W2, and W3. It doesn't matter about the blacks.

Since we know we have a white it could be W1, or W2 or W3.

If it is W1, then the other marble is also white (W2).

If it is W2, then the other marble is also white (W1).

Only if it is W3 is the other marble B.

So there are 2 chances out of 3 of getting a white, not 1 chance in 2. Sorry.

Bob

]]>I liked this problem. Post more of these!

]]>