Brain Teaser No 1

Coincidence.....or ???

You don't think Mick is going to shoot Matthew do you? They've been a touch at loggerheads in the past, you know.

Oh dear. There I go again.

I pick two manes, purely at random of course!, just to add a bit of 'character' to the old maths problems, and all of a sudden we have talk of attempted murder....what sort of imagination have you got, JonR ??

I should have added the usual qualifyer.....all characters are purely fictional [well that bit's true whichever way you look at it!] and any resemblance to persons living or dead [!] is entirely coincidental.....

Believe that and you'll believe anyth....

Cheers

Don

"...and all of a sudden we have talk of attempted murder....what sort of imagination have you got, JonR ??"

Hmm...you have a point, Don. Perhaps someone should lock me in the Padded Cell and throw away the key!

JonR

quote:

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Test to Destruction....)

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Man I'm really going to have to try and dig out my old A-level maths/physics books to answer that one, it took me some time to remember enough maths to do the max box problem and what good has it ever done me...

Man....it took me some time to remember enough maths to do the max box problem and what good has it ever done me...

so, you never made it to the dizzy heights of:-

Naim Packaging Manager required

7 days a week, 364 days a year (Xmas holiday)

Minimum wage honoured.

Cheers

Don

Test to destruction...

Two-Sheds...

all you need is a bit of resolution to get started.....then I'm sure you'll accelerate to a rapid conclusion in no-time (Newton) at all.....gee....whiz.

Cheers

Don

[This message was edited by Don Atkinson on Sat 29 May 2004 at 23:16.]

quote:

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Elementary problem that requires coefficient of friction to be known

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I'm assuming that when Don said

quote:

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A mass of 30 kg (the competitor's latest preamp) is placed on a smooth horizontal table

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that there is no friction.

A couple of reminders.

Newton identified that an external Force F, acting on a body of Mass M. will produce an acceleration 'a' of the Mass, such that F = Ma

Mass M acting down generates a Force due to gravity 'g' (acceleration) such that F = Mg

If mass M is placed on a horizontal table and pulled horizontally, friction 'f' will resist such that f = μMg where 'μ' is the coefficient of friction, which is a dimensionless value and usually obtained by experiment.

In the question given, I tried to simplify the situation by referring to a 'smooth' table and peg plus a 'light' 'inextensible' string. The smooth table implied no friction ie μ = 0. Likewise the peg. (Well spotted Two-Sheds) And the light inextensible string was designed to avoid complications with the bag of cement acting like a bungee jumper!

Cliff has presented a very good solution and explanation, taking into account friction. And as he says, it is all very elementary !..... Only, like Two-Sheds, most of us have forgotten all this elementary stuff, we vaguely remember the QUESTIONS but the ANSWERS....

At the risk of repeating Cliff's work, my answers are set out in my following two posts. First, ignoring friction, on the basis that the table is smooth and that this presents a 'simple' solution which might be easier to recall. Second, my version of Cliff's general solution taking friction into account. This second solution, which is the same as Cliff's, reduces to the first solution simply by setting the coefficient of friction to zero.

I hope this will all bring back happy memories of applied maths or physics and golden memories of school and a happy childhood....and they all lived happily ever....

Cheers

Don

PS, I will wait a little while before posting just to give others a chance to do the 5 or 6 lines of arithmetic assuming friction = zero

Testing to destruction

The teflon version

F = ma (Newton's 2nd law)
Let Tension in string = T
Let acceleration of system = a

Resolve horizontally
T = 30a
a = T/30 (1)

Resolve vertically
50g - T = 50a (2)

Sub for 1 in 2

50g - T = 50T/30
50g = 80T/30
T = (50*30*g)/80
T = 184 Newtons

As Cliff said, elementary.
Unless your maths is a bit rusty, in which case things get a bit stickey....see the next version

Cheers

Don

The non-teflon version

Let Tension in string = T
Let acceleration of system = a
Let large Mass (cement) = M
Let small mass (preamp) = m
Let coeficient of friction on table = u (Greek letter pronounced 'mu')

Resolve horizontally
T - μmg = ma
a = (T - μmg)/m (1)

Resolve Vertically
Mg - T = Ma (2) (note m is resisted by the table)

Sub for 1 in 2

Mg - T = M(T - μmg)/m
Mg + Mμg = (MT/m) + T
Mg(1 + μ) = T(M + m)/m
T = Mmg(1 + μ)/(M + m) (3)

Which is the answer Cliff provided

If μ = 0 them eq 3 can be reduced to
T = Mmg/(M + m)
and if M = 50; m = 30; g = 9.81 then
T = (50*30*9.81)/80

Cheers

Don

For those who missed it first time around.....(a day or two back)

Yet another hifi factory in Salisbury

Matthew R and Mick P have both got Saturday jobs at a hifi factory in Salisbury. Matthew, so he can earn a bob or two to fund his anti-war marching campaigns and Mick so he can buy another gun. Both cycle to/from work....but that's another story....

Paul D has completed his time and motion studies on the pair and found that Matthew takes 8 hours to test 50 Nac 552 preamps whilst Mick can test the same number in 6 hours. How many hours (to 4 sig fig) will it take them to test a batch of 100 between them, starting together, but working independantly. (tea breaks, coffee breaks etc and time out for cosy discussions about politics can be ignored)

Cheers

Don

An astonishing coincidence...or what?

I was browsing through a couple of books on recent history and politics the other day, dealing with the Cold War era and noticed the following remarkable coincidence....

John F Kennedy was born in 1917 and became President of the US of A in 1961. When he was assassinated, he was 46 years old and had been President for 2 years. Now, totting up these numbers, I got the unremarkable sum of 3,926.

But wait....

Khrushchev was born in 1894 and became 'Top Man' of the USSR in 1958. When Kennedy was assassinated, Khrushchev was 69 years old and had been in power for 5 years. The sum of these numbers....you've guessed it... the unremarkable sum of 3,926.

Well, I thought, as I stared to read about Charles de Gaulle, wouldn't it be a coincidence if...Yes.....he was born in 1890 an he did become President in 1958 and when Kennedy popped his clogs, de Gaulle was 73 and had been President for 5 years, and.....YES these numbers add up to the now remarkable sum of 3,926...

An astonishing coincidence...or what?

Cheers

Don

Cliff,

Hope you enjoy the train journey. Afraid I can't help you with pub/lunch recommendations, but hopefully someone else will read your other thread.

I am impressed with the way people keep connected whilst travelling these days, but surely the Nothumberland coastline is more interesting than the Padded Cell?

Anyway, I've posted another mind-blowing teaser that might keep you ocupied for a minute, possibly two.

Cheers

Don

quote:

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An astonishing coincidence...or what?

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'Or what'

Curious that 3926 is 1963 + 1963.... Or not.

Paul

Paul,

you are pointing in the right direction.

Or did you know that already.....

Cheers

Don

quote:

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John F Kennedy was born in 1917 and became President of the US of A in 1961. When he was assassinated, he was 46 years old and had been President for 2 years. Now, totting up these numbers, I got the unremarkable sum of 3,926.

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If we write down the components of the unremarkable sum,

1917 + 1961 + (1963 - 1917) + (1963 - 1961) = 3926

we see that the birth year and accession to power mysteriously vanish in the mix. I think we can count coincidence out.

Paul

Paul,

we can certainly count coincidence out. you are walking around the logic. and, as so often, it is obvious (once you see it) and you might even have seen it.

Cheers

Don

Don,
I'm fairly sure that Paul has already sussed it, but just in case...
The "coincidence" is caused by a clever use of words. The words, when unravelled, simply add 1963 plus 1963, ie they are just another way of arriving at the year of JFK's assassination.

Regards,

Steve D

I was being obscure for the joy of obscurity.

Or perhaps that should be 'obtuse'.

Paul

Redgirl,

I don't think I can explain Benford's Law at all, never mind simply. However, John provide a link that did describe Benford's Law and provided a mathematical explanation of associated probabilities. In case you didn't notice the link I have copied an abstract from the article which at least describes the law.

The article makes it clear that whilst there is good reason to expect the results we see, they are not guaranteed

"A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, etc., the digit 1 tends to occur with probability , much greater than the expected 11.1% (i.e., one digit out of 9)."

The probabilities tend towards the following;-

1 0.30103......6 0.0669468
2 0.176091.....7 0.0579919
3 0.124939.....8 0.0511525
4 0.09691......9 0.0457575
5 0.0791812

Probably not much help......

Cheers

Don

[This message was edited by Don Atkinson on Thu 03 June 2004 at 20:49.]

I'm fairly sure that Paul has already sussed it, but just in case...

yes, I was fairly sure as well, Paul is very decent at giving opportunities to others.

Yes, If you note the date of an event, (1963) you don't need to actually quote that date. If you were born in 1946 and were 17 years old when Kennedy was shot, or born in 1917 and were 46 years old when you were shot, well you always generate 1963 with that pair of numbers.

Likewise if you were elected President of the Brunel Borough of Swindon in 1957 and had been in Office for 6 years when Kennedy was shot etc etc.....

But it does appear to be a bit of a coincidence to some.......

Cheers

Don

Splat !

Mrs D started thinking this evening......always an ominous sign.

"Suppose" (Oh dear!) she said, "Suppose, a fly was flying along a road in one direction, and got hit by my car doing 80mph in the opposite direction.."

"SPLAT!" is what I thought, but instead said "Yes dear".

"Well," continued Mrs D "after its been hit, the fly that is, it has reversed its direction of travel by 180 deg, or at least the fly-goo has"

"I doubt if the fly is actually aware of this" is what I was thinking, but instead said "Yes dear".

"OK" said Mrs D, which is an even more ominous sign, and I could see she was thinking really hard now, "Which means that, at the instant in time it changed direction, the fly must be stationary".

"Well, yes dear" was what I was thinking, but instead, sensing some sort of 'coup-de-grasp' simply said "Go on dear"

"Well," she said "at that same instant, it is also stuck to the windscreen and the car, so the windscreen and the car must also be stationary, but they weren't. So there seems to be some sort of anomaly here"...

"Yes dear, and I know what that anomaly is" is what I thought, but "How about a nice cup of tea, dear" is what I said.

"Chaps", (as Mick P would say), I do need answers pretty quick for this one...

Cheers

Don

ISTM it's all relative.

Paul

ISTM it's all relative

Mrs D is my dear wife....is it that kind of relative we are talking....

or is it Newtonian relative or Einstienian relative....

or the 'relatively simple' sort of relative...

or....

the typical Paul Ranson "slow relevation" (or should that be revelation?)

Cheers

Don

Not sure how much serious to be, anyhow...

Well, its not the most serious thing in life, (unless you're a fly), but its a serious teaser that invites thought and an explanation.

The fly is "elastic" it shrinks when it hits the windshield, when it changes direction it still shrinks

....it can't keep on shrinking forever....sooner or later each bit has to reverse direction and therefore sooner or later each bit has to stop for a moment...

cheers

Don

Omer,

Not sure how much serious to be, anyhow

the original version of this (from my perspective) appeared in New Scientist some while back and invited serious explanations, which it got.

The subject needs a bit of relatively careful thought,

Cheers

Don