Question

Please use "mathematical Induction".

If there are n participants in a knock out tournament then prove that n-1 matches will be needed to declare the champion

Answer 1

Iam, are you there?

Answer 2

Yes, Sir

Answer 3

If we solve it in this way.............

Answer 4

lets say that the thing is correct for k players, So we can say that k-1 matches are required to find a champion

Answer 5

So now, for k+1 player, we can say that to find out a winner out of k players we need k-1 matches

Answer 6

And the winner can play a game with the last one, so in all we need k matches

Answer 7

This is the way I solved the problem

Answer 8

But I think its not keeping the term "knock out" in place

Answer 9

Pretty much.

Answer 10

I mean, in a knock out match we can't say that there is a last player, and that player is playing with the winner of all the previous games

Answer 11

So this why I think my solution is incorrect

Answer 12

Well, I kind of liken these problems to geometrical ones where you're needing to show general properties via an assumption on a whole portion beforehand. We add a component to the end and work through the final leg of induction at that point.

I see what you're saying with the knockout thing, but I have a suspicion there's a symmetry at play here, which means in the end, it doesn't matter if you attach the last player at the end.

I'll have another look.

Answer 13

So your present view point is "I am correct"

Answer 14

Yes

Answer 15

But I am going to take a look at it using combinatorics.

Answer 16

I will be very much pleased if you do so

Answer 17

Okay. I have to finish preparing a lecture. I'll see what I can sort out. Did you finish the parabola problem?

Answer 18

Actually it was out of the scope of my syllabus. But still I did

Answer 19

good

Answer 20

I got it from the internet

Answer 21

But one thing I must tell you, among all the people I talked about the problem, you were the only one who had some idea

Answer 22

Well, good to hear...I guess. I've been extremely busy this week.

Answer 23

Some suggested that there was not enough information, and some said that the curve was just touching the x axis

Answer 24

Yes, I felt that you were busy, because I hardly saw you

Answer 25

No. You have to perform a linear transformation and a rotational one. At least, that's what I'd do, and invert.

Answer 26

Is this not just a permutation problem?

Answer 27

Yes I understand that, and without that rotation the problem looses all its fun

Answer 28

It becomes a trivial one

Answer 29

fun...watch out STEP

Answer 30

Any how thank you for all your time. And I will surely wathc out for STEP

Answer 31

*WATCH

Answer 32

If you could advice me on how to increase my concentration span, I would be very grateful

Answer 33

Not now (if you are busy)

Answer 34

Ha! If I knew that, I could help myself. I have the attention span of a gnat.

Answer 35

But some time later (when you have some time to spare)

Answer 36

LOL

Answer 37

The only things you can do are exercise and sleep and eat.

Answer 38

and maybe meditate, but I don't do that so I can't really comment.

Answer 39

I found that its all about the concentration span that separates the best from the rest

Answer 40

I mean I felt

Answer 41

And being the best, I though may be you will have some secret

Answer 42

And being the best, I thought may be you will have some secret

Answer 43

If you want a tip on taking cognitive ability tests, time yourself and don't spend too long on one question.

Answer 44

can u plz spare some thought on my question as well?

Answer 45

No, unfortunately, there're no secrets.

Answer 46

Just like everything else

Answer 47

Yes.

Answer 48

rsaad2, is your question about rain?

Answer 49

yes.

Answer 50

our cal with theory instructer mentioned it. i could not find the required info on internet

Answer 51

are you studying calculus of variations?

Answer 52

e.g. functionals?

Answer 53

no. its calculus with theory.

Answer 54

we were studying line integrals. so he mentioned itthere.

Answer 55

OK. If this is something you can leave me with, I may be able to look later. I have to do some prep. work for tomorrow. Is this for an assignment?

Answer 56

sure. no its not for an assignment.

Answer 57

ok. i'll look at it later.

Answer 58

thank you. =)