Doing things the hard way

ColinM

On Countdown today on Channel 4, a contestant (for reasons best known to himself) decided to ask for 4 large numbers and 2 small ones.
The numbers drawn were as follows: 100, 75, 25, 50, 1, 2
The target was 253.

Both of the contestants had a good long think about this one, and only raised their heads after at least 15 seconds had already elapsed. Both had knowing smiles, intended to indicate that they both knew the answer and found it humourous.
Can you guess what the solution offered by the female contestant was?
It wasn't the obvious one. This was her actual answer:

(100x2) + (75/25) + 50 = 253 !!

Well, I was thinking of saying something flippant, like "trust a woman to do something the hard way".

Then I thought of something more constructive. How often does something like this happen in advanced mathematics? Is it possible that the elusive answers to many of those unsolved "last theorems" are staring us in the face, but we don't see them because we are expecting the solution to be complicated?

Does this happen in other areas, such as science or engineering, or even with matters relating to the human condition?

I'll stop now before I get too philosophical. I have actually noticed though, that a lot of mathematicians tend to be quite fanciful rather than rigorously mundane (which is what you might expect).

GuanYin

Originally posted by ColinM
Then I thought of something more constructive. How often does something like this happen in advanced mathematics? Is it possible that the elusive answers to many of those unsolved "last theorems" are staring us in the face, but we don't see them because we are expecting the solution to be complicated?

What, that problems have more than one solution? Hehe, did you ever consider that the advanced mathematics is the easy way??

I've seen some alternative proofs for theorems before(presented in a sort of lay persons way), I think one was a sort of gag one, I don't remember them though. Anyone know any?

Originally posted by ColinM
Does this happen in other areas, such as science or engineering, or even with matters relating to the human condition?

Observing in work, people will always do things the easiest way possible.

Students in exams and tutorials, from what I've seen, often attempt to do things in the most mind-numbingly complicated and confusing way possible.

Lafortezza

Originally posted by syke
Students in exams and tutorials, from what I've seen, often attempt to do things in the most mind-numbingly complicated and confusing way possible.

probably trying to show the examiner that they *know* the most complicated way of doing things, ie "give me full marks!!"

I remember seeing a webpage somewhere that had lots of proofs of theorems like
"2+2 not equal to 4" and lots of other nonsensical stuff,
must give it a google when I get time

angelofdeath

would,ve been easier to add them all together, but some people like a challenge or maybe she just completly missed the obvious, it can happen you know:(

sceptre

Originally posted by ColinM
Then I thought of something more constructive. How often does something like this happen in advanced mathematics? Is it possible that the elusive answers to many of those unsolved "last theorems" are staring us in the face, but we don't see them because we are expecting the solution to be complicated?

There certainly have been quite a few examples of theorems with complicated proofs being proved in a far simpler way. That book about Paul Erdos ("The man who loved only numbers") which I'm reading this week (recommended by ecksor so I thought it would at least be worth getting out of the library) before going to sleep mentions a few examples.

Capt'n Midnight

Wasn't there that simple proof of a 2000 year old axiom about lines and points. 2000 years it was classed as an axiom 'cos no one could prove it - yet the proof could be done in pass maths.

ecksor

That doesn't ring a bell with me, and I've read a fair bit of maths hisory ... Can you supply more information?

The only similar example I can think of is the attempts to prove the parallel postulate from the other axioms within euclidean geometry, but then Gauss and others showed that there were perfectly valid forms of geometry based on the other axioms that didn't depend upon the parallel postulate.

Cake Fiend

Originally posted by ColinM
a lot of mathematicians tend to be quite fanciful rather than rigorously mundane (which is what you might expect).

Surely it's far more interesting to take the path less followed rather than do things the same way everyone else does? Besides, don't you get more points in countdown for using as many arithmetic symbols as possible (it's been a number of years since I've watched countdown, so I could easily be mistaken)?

Originally posted by lafortezza
I remember seeing a webpage somewhere that had lots of proofs of theorems like
"2+2 not equal to 4" and lots of other nonsensical stuff

IIRC a lot of these 'weird' proofs use little tricks like dividing by zero to give their (wrong) answers.

Syth

Many of those 'proofs' rely on dividing by zero, but not all do example

sceptre

Originally posted by Sico
Besides, don't you get more points in countdown for using as many arithmetic symbols as possible (it's been a number of years since I've watched countdown, so I could easily be mistaken)?

Naw, if you work it out you get your ten points. If no-one works it out the person closest gets the ten points.