Experimental Mathematics Troll

Bob · 2014-10-23 19:48:17

Simplest solution:

I thought of this early on but rejected it as not working. Now I can see it does work. Shame I didn't have more confidence back at post 50 or so.

If there are no restrictions then the number of orders is 6! = 720.

Now look at the guardian pairs like this

G1 G2 C1 G3 C2 C3 and
C1 G2 G1 G3 C2 C3

In this pair of solutions four of the positions are repeated and I have just swapped G1-C1

Now introduce the guardian first restriction. For every pair like the above, one solution is allowed and the other isn't. So divide by 2.

This reduces the number of solutions to 720/2 = 360.

Further reduce by 2 and 2 to removed the 'not-allowed' C2-G2 pairs and the C3-G3 pairs.

Final number of solutions = 360 /2 /2 = 90.

Bob

Last edited by Bob (2014-10-23 19:50:22)

Agnishom · 2014-10-23 19:56:14

Solutions by Brian

There are a few approaches to solving this problem.

- Method 1:

Choose one of the \(3\) children to put last; then their guardian can be placed in one of the \(5\) time slots before their child. In the next available time slot prior to that of the child in the last time slot place one of the remaining \(2\) children; their guardian can then be placed in one of the \(3\) remaining time slots before their child. The remaining two time slots can then be filled in only one appropriate way, (i.e., the remaining guardian prior to their child).

This gives us a total of \(3*5*2*3 = \boxed{90}\) interview orderings.

- Method 2:

For any given guardian/child pairing, half of all interview orderings will have the guardian interviewed prior to the child. Since this is the case for each pairing, we have that \((\frac{1}{2})^{3} = \frac{1}{8}\) of all orderings will have each guardian come before their child. Since there are \(6! = 720\) possible orderings, we have \((\frac{1}{8})*720 = \boxed{90}\) orderings that satisfy the given restriction.

- Method 3:

Label the guardians/children as \(A, A, B, B, C, C\). We don't actually have to distinguish between the guardians and their children in this labeling process, since when we permute these \(6\) letters there is only one permitted way of ordering each guardian/child pairing. So the number of allowed orderings is the same as the number of permutations of these \(6\) letters, which is \(\dfrac{6!}{2! * 2! * 2!} = \dfrac{720}{8} = \boxed{90}\).

Well, I asked the Amazon people a more interesting problem: Is there a set whose cardinality is strictly between that of Real Numbers and Integers?

Arna · 2014-10-23 20:01:46

I posted a disputed problem and the solutions are coming up still now
How amazing is the magic of maths!!

bobbym · 2014-10-23 20:06:58

The answer is 6 and I was marked wrong!

Agnishom · 2014-10-23 20:09:51

I am extremely sorry. That should have been 6 instead of 8.

Arna, can you please delete it and post it again

Well, as I told you it's (2+1)*(2+1)*(2+1)=27

I thought there are four twos. I counted it wrong

Last edited by Agnishom (2014-10-23 20:11:39)

bobbym · 2014-10-23 20:13:18

4 down from the top and 2 on the side.

Agnishom · 2014-10-23 20:16:12

Do you think I should ask her to delete it and repost or should I ask Calvin to update the answer?

bobbym · 2014-10-23 20:19:12

Do what causes you the least harm. I am not that mad about it. But I would like to get my 100 points. I do not understand why after I was marked wrong the rating went down? It should have gone up. Arpad Elo is an imbecile.

Arna · 2014-10-23 20:20:45

Reposted the problem

bobbym · 2014-10-23 20:22:24

Where is it?

Arna · 2014-10-23 20:23:55

search my profile you'll get it

Agnishom · 2014-10-23 20:25:54

It should appear in your feed (reccomended page) now, and also look at level 2 in the popular geometry problems

Do you mind following arna?

Last edited by Agnishom (2014-10-23 20:28:13)

bobbym · 2014-10-23 20:29:17

I will follow her.

Arna · 2014-10-23 20:55:41

thank you for following me bobbym

bobbym · 2014-10-23 20:56:50

What are the advantages to being followed?

Arna · 2014-10-23 21:02:26

Nothing.
But seeing someone you respect follow you makes us happy at least makes me happy

bobbym · 2014-10-23 21:05:35

This respect guy, who is he?

Arna · 2014-10-23 21:06:37

Actually I respect all those who love Maths
and that includes you too!

bobbym · 2014-10-23 21:07:36

Hahhahhahahahha, I have fooled you then. I hate math.

Arna · 2014-10-23 21:09:43

see perception again comes to the rescue
In your view you hate maths
but in my view you love maths
see how that all differs?
Again in your view you have fooled me
but in my view you did not fool me!!
Anyways everyone fools me as I am very stupid

bobbym · 2014-10-23 21:13:02

Anyways everyone fools me as I am very stupid

You are 13? You are not stupid.

Arna · 2014-10-23 21:14:48

yes I am 13

bobbym · 2014-10-23 21:18:30

At least you are not a bumpkin.

Arna · 2014-10-23 21:19:45

well again perception takes over
Define bumpkin?

bobbym · 2014-10-23 21:23:21

A derogatory term used to describe a backward country person. One with no class or education.

Math Is Fun Forum

#76 2014-10-23 19:48:17

Re: Experimental Mathematics Troll

#77 2014-10-23 19:56:14

Re: Experimental Mathematics Troll

#78 2014-10-23 20:01:46

Re: Experimental Mathematics Troll

#79 2014-10-23 20:06:58

Re: Experimental Mathematics Troll

#80 2014-10-23 20:09:51

Re: Experimental Mathematics Troll

#81 2014-10-23 20:13:18

Re: Experimental Mathematics Troll

#82 2014-10-23 20:16:12

Re: Experimental Mathematics Troll

#83 2014-10-23 20:19:12

Re: Experimental Mathematics Troll

#84 2014-10-23 20:20:45

Re: Experimental Mathematics Troll

#85 2014-10-23 20:22:24

Re: Experimental Mathematics Troll

#86 2014-10-23 20:23:55

Re: Experimental Mathematics Troll

#87 2014-10-23 20:25:54

Re: Experimental Mathematics Troll

#88 2014-10-23 20:29:17

Re: Experimental Mathematics Troll

#89 2014-10-23 20:55:41

Re: Experimental Mathematics Troll

#90 2014-10-23 20:56:50

Re: Experimental Mathematics Troll

#91 2014-10-23 21:02:26

Re: Experimental Mathematics Troll

#92 2014-10-23 21:05:35

Re: Experimental Mathematics Troll

#93 2014-10-23 21:06:37

Re: Experimental Mathematics Troll

#94 2014-10-23 21:07:36

Re: Experimental Mathematics Troll

#95 2014-10-23 21:09:43

Re: Experimental Mathematics Troll

#96 2014-10-23 21:13:02

Re: Experimental Mathematics Troll

#97 2014-10-23 21:14:48

Re: Experimental Mathematics Troll

#98 2014-10-23 21:18:30

Re: Experimental Mathematics Troll

#99 2014-10-23 21:19:45

Re: Experimental Mathematics Troll

#100 2014-10-23 21:23:21

Re: Experimental Mathematics Troll

Board footer