And then there is the lawyer who shows the girl a big diamond, and she goes to him.
John

 

Engineering is the perfect discipline for me. It's got exactly the right proportion of theory and practical, and enough "gray areas" to keep me challenged. And, there's always an interesting problem to solve.

This reminds me of a joke I am sure you've heard many times before:

An engineer and a mathematician are each placed in the corners of a square room. A beautiful girl stands in the middle, exactly half way between the two.

They are given instructions: Each can move to a position half way between their current position and the girl at a rate of one move per minute. When they reach the girl, they can kiss her.

The mathematician is despondent. When asked why he is so upset, he says, "But I'll never reach her!"

The engineer smiles. He says, "I'll get close enough."

Yep. The variant I always liked goes like this:

At a high school career day all of the kids are assembled in the gym and the principal, a former science teacher, wanting to get things off to a more active starts, says, "Today you will have a chance to visit with people from many different fields and one thing I want you to see is that people in different fields think about the work differently. So I've asked three of our visitors, a mathematician, a physicist, and an engineer, if they would be willing to solve a problem for you. So I want all of the boys to go to the west end of the gym and all of the girls to go to the east end. Then, each minute you will move one half of distance between where you are and center court. So how long will it take for you to come together? Let's ask our guests, in turn, for their thoughts."

The mathematician responds, "They will never come together."

The principal smiled as this was exactly the answer he wanted to hear.

The physicist responds, "It will take an infinite amount of time, but they will come arbitrarily close to each other."

The principal smiled as this was exactly the answer he wanted to hear.

The engineer responds, "In less than ten minutes they will be close enough together for anything that they might have in mind."

The students smiled as this was exactly the answer they wanted to hear.

 

Fortunately, I like to argue.

So I have provided you with ample opportunity.
That service is not, however, free.
I will post the bill tomorrow.

Meanwhile since you like changes to the rules here is a variation of your problem.

Four trained fleas stand at each corner of a square of side one unit.
Each flea faces the next one round the square in a clockwise direction.
At the click of the ringmaster's fingers each flea begins to hop directly towards the next flea it is facing.
At all times each flea hops directly towards the next.

The four fleas thus hop a spiral path and meet in the middle of the square.

How far does each flea hop?

 

How far does each flea hop?

Answering your questions is futile. You'll just insist I'm wrong, but not why, and you will refuse to submit your own solutions for critique. In fact, any answer you provide will have come from committee, and will be pending clarification of the original problem into perpetuity.

Over the course of this thread, I have completely lost the desire to party with you. To do so would be infuriating. TIFWIW.

 

As an aside, I'll always remember my first college prob/stats course as being an exercise in which the instructor first demonstrates that the students do not, in fact, know how to count.

Could you tell more about this in particular?

 

Could you tell more about this in particular?

Oh, it's really just the same kind of counting that this problem is all about. You're given strange problem descriptions about how many balls of different colors are in a box and how they are selected and how many are selected and then ask what the chances are that you will have between this many and that many balls of a certain color when you are done. It seems like it should be easy, but it gets really hard to keep track of things properly pretty quickly. On the first exam, which is purely discrete prob/stats, the scores were so low that they gave a make-up test to the whole class.

 

...

I use my designs to check the computer...
...

You always surprise me with your comments/answers... LOL

 

...

This is starting to feel like the arguments I have with my wife. She asks a question for which she thinks she knows the answer, and then argues that I must be wrong because I answered the wrong question.

Fortunately, I like to argue.

LOL... Yes you do Big time!

 

I really have enjoyed reading the whole thread from post #1.

Good job WBahn, joeyd999 and djsfantasi!

Still waiting for Studiot *detailed solution* or I'll give it a shot too!

 

I really have enjoyed reading the whole thread from post #1.

Good job WBahn, joeyd999 and djsfantasi!

Still waiting for Studiot *detailed solution* or I'll give it a shot too!

Which reminds me. Today is the 5th day after tomorrow!

 

So I have provided you with ample opportunity.
That service is not, however, free.
I will post the bill tomorrow.

Meanwhile since you like changes to the rules here is a variation of your problem.

Four trained fleas stand at each corner of a square of side one unit.
Each flea faces the next one round the square in a clockwise direction.
At the click of the ringmaster's fingers each flea begins to hop directly towards the next flea it is facing.
At all times each flea hops directly towards the next.

The four fleas thus hop a spiral path and meet in the middle of the square.

How far does each flea hop?

I think it would be more appropriate for you to post YOUR long promised solution to the problem YOU posted in the first place.

Your new problem is very poorly defined. How far does each flea hop each time? It has a HUGE effect on the answer. Don't think so? Imagine each flea hops 0.99 units each time, meaning that at each hop they end up almost where the flea in front of them left from. Or, imagine that they hop 1 unit, in each case they hop from one corner to the next indefinitely. So before we waste our time on another puzzle that you probably won't post your solution to (though, in all fairness, you haven't promised to ever post a solution for this one, I notice), please go check with the appropriate exam committee to clarify what they intended.

 

I was wrong.

It is now a week and I have not heard any more and I cannot think of a plausible additional condition why the fourth character should be restriced to 2 in the 'official' solution.

5*24*23*2*9*8

Which is exactly half the solution shown by WBahn in post#9.

I concentrated on vindicating the official solution, instead of trying to solve it myself, but agree that the post#9 method is how I would normally go about it.


It has, however given the subject of passwords as good airing and I have learned something.

 

BTW: For your spiral problem assuming that the fleas move directly toward each other at all times (i.e., infinitesimal hop distance), I got a total distance traveled of 2 units.

 

I trust I am not too late to the party. My brain started to hurt trying to confirm how joeyd worked the problem, so I did it a way my brain can handle.

I see 4 ways to pick the letters:

V C C V N N
V V C V N N
V C V V N N
V V V V N N
The total count is the sum of these possibilities:

V  C   C   V  N  N  
5  21  20  4  9  8  604800
  
V  V   C   V  N  N  
5  4   21  3  9  8   90720
      
V  C   V   V  N  N  
5  21  4   3  9  8   90720
    
V  V   V   V  N  N  
5  4   3   2  9  8    8640
  
            Total:  794880

There. I agree with joeyd.