Math Is Fun Forum

Right I have now sent an email from the gmail account. See if you have got it....

Okay I will send a very short email to you now.
Right done that.

Also have you read the post above by the way ?

I have sent another email in which I have copied and pasted the exact form of that email address above and as far as I can
see it is exactly the email address I have been using to email you for about 4 months.

EDIT: Following a recent test email to myself I think that my email software thinks that my
own email is spam. This supports the anti-spam software theory, but does not prove it.
For my email to you it would be most likely your email provider and your email software that
might class it as spam possibly also your ISP if different to the email provider.

I have edited post #1171 with my latest theory, but really I don't know at the moment.

I am going to try pasting this post into an email to see if you can get it. Let me know what happens.....

I am not sure, but I think that your email receiving is accidentally deleting many of the emails I send.
I did send them, but you say that you have not got them.

Anti-spam software is not perfect it could very easily class a non spam item as spam,
or class a piece of spam as not spam and let it through.

With the email software I have it lets me choose what to download based upon headers - usually everything.
I have known the occassional good email get classed as spam by the email software.

Also ISPs do sometimes delete massive amounts of spam using clever software of their own.
I wonder if they have accidentally deleted some of my emails to you. If so I cannot do anything about it.

Also I notice that you have used two computers to send email on (if I am understanding things correctly).
Therefore are you always checking both computers when you receive an email ?

Okay I will try again.

I am not sure exactly which bit you are stuck on but make sure you deal with ALL cases.

In other words something like:

(1) Suppose the customer borrows before the peak rate starts, but returns before the peak rate starts.
(2) Suppose the customer borrows before the peak rate starts, but returns after the peak rate starts, but before it ends.
(3) Suppose the customer borrows before the peak rate starts and returns after the peak rate ends.

(4) Suppose the customer borrows during the peak rate period and returns during the peak rate period.
(5) Suppose the customer borrows during the peak rate period and returns after the end of the peak rate period.

(6) Suppose the customer borrows during the period after the peak rate and ends the loan after the peak rate.

(7) Suppose the loan occurs over 1 day, 2 days, more than 2 days.

In each case make sure you test the condition, use an if statement (not sure how that works in PHP), and does the right
thing in each and every case. The time periods concerned can be done by simply (end time of section - start time of section) in
seconds, and then converted by a factor if needed, remembering to add together all of the chunks if appropriate, if there is only
one piece of time then it is just the one bit, but if there are several then I'm afraid you have go through them somehow and add them.
No maths function is really going to help. So a computer program is needed using if constructs, procedures, method calls,
(or whatever is used in PHP) or whatever is appopriate in the language(s) used.
I suggest setting up variables and constants with meaningful identifiers for ALL of the relevant things to do with time
and rate of charge for each printer.

I am not sure whether you realised that the time stamps appear to be seconds since 01/01/1970.
I apologise if any of that is wrong so double check all of it if it is for a serious purpose like a real business or serious Computer studies.

Hi. Yes the weather is hot in the UK another 29-30C heatwave. The grass is getting rather dry.
Anyway I am ready to explain some maths when you are...

tan(30) is 1/(square root of 3)

Not sure what is special about Tan(85). Looks like a rather horrible irrational number even when squared.

I do notice though that the other two multiply to leave 1.
(Tan(25) * Tan(65) = 1 I presume atran's trig. result proves it. Is this because 25+65 =90 ? and Tan(90-x) * Tan(x) = 1 etc.)

I notice that the gap between 85 and 90 is only 5. This is one sixth of the gap from 30 to zero.

I can tell from calculating the answer that it is not going to give us a whole number or the square root of a whole number.
Any idea what you are supposed to be trying to prove?

I have noticed that the angles 85 + 30 + 65 = 180

The three angles are interior angles of a triangle. I am not sure where this leads or whether it is relevant.

Okay here goes my attempt at a strange nested multiple choice question:
(I may have to work on this one a bit because this is rather improvised.)
If this is a multiple choice question:
(
  If this is a multiple question:
What is the probability of a correct answer to this
(1)    25%
(2)    0%
(3)    25%
(4)    50%
)
What is the correct reason:
(1)    None of the available options are 100%
(2)    It is a recursive paradox
(3)    It is impossible, but 0% is an answer
(4)    25% is mentioned twice ambiguously
(5)    50% is also mentioned in case you are arguing that since 25% is there twice the answer is 50% this is also there so is 100% correct if this is your argument. 33.3 recurring is omitted.
(6)    All of those
(7)    The probability of this question being sound is not very high
(8)    The probability of this question being answered right is not great
(9)    Sorry that one was a comment not an option.
)
For the above how likely are you to get the answer to the outer bit right as a percentage?

I might have to work on that. Face it if you have chosen an answer then you have decided that it is 100% correct. You are therefore right and also wrong.
They should have that as an entrance question for something.
I always thought that mathematicians told the best jokes. That was a bad question on a number of levels.

It is possible to have an UNSOUND multiple choice rather than simply one that could be had to have "a non 100% percent chance
of you being considered correct by an infinitely* intelligent (imagined) person". (* = impossible in practice)

I have encountered this concept before, but for obvious reasons I shall not give a real example.

However I could easily make up a deliberately flawed multiple choice question about a factual subject:

What is the capital of France:
(1) Red
(2) Blue
(3) Purple
(4) Orange

Well none of them because all of those are colours, and we wanted a town for strarters, and we know that Paris is correct.
(Maybe there is a very very small chance that one could be argued to be correct due to a highly eccentric pseudo-course,
but if it were an ordinary thing like an exam then it would be an accidental error and considered unsound.
Bad for an exam because no student could ever be certain of getting the answer right about a matter of fact,
but on the other hand perhaps a strange history course might have said that a colour were the answer at some
point in history. Obviously this is NOT true, but if it were then it might be possible if that insight were both known and true.)

The question is not simply difficult, but impossible, because none of the choices is a satisfactory answer.

I would say that although you have created a very clever and amusing brain teaser in mathematics my answer would be:

Just like the above answer, although there is a paradox in yours and no paradox in mine, your question is a deliberately
unsound multiple choice in which is very possible that if you were to take a survey and work out a rough estimate of the
number of people that give the answers shown you could very easily get no answer at all being correct.

On the other hand: I suppose it could be that by an amazing coincidence one of them IS in fact correct fundamentally,
in which I may have to work upon my own definitions to make that better because otherwise a rare exception might
give a valid answer, but you would have to be Mystic Meg* to know what the answer would be.
(Not allowed for a hypothetical exam, but in terms of a brain teaser the questioner has a "licence" to think creatively.)

* = Replace with any fortune teller name of person thought of as able to predict the future precisely.
Mystic Meg is often used informally in the UK to refer to an imagined person able to predict the future to be able to
say "I'm not Mystic Meg" instead of "I am not a magician" and so on in appreciation of an astrologer with this psuedonym.
(Some of my questions are unsound by accident to be fair. None of us are right always.)

I think what I had meant really is perhaps initially to help understand things work out the distribution formula/formulas
of the maximum of the 12 values for the numbers in each month when distributed as you would expect when putting
1000 individuals randomly into the 12 categories.

Then to use this to work out the 99th percentile of the maximum of an arbitrary instance of 1000 individuals being randomly (uniformly)
put into 12 categories, or even according to the actual proportions of the months taking into account the exact number
of days. (The bit above is not really needed, but probably a good idea to try first if one were to try to calculate it exactly.)

Maybe it is better to say "Work out the 99th percentile having found a formula for the distribution of the maximum of a
given set from which 1000 people have been put into 12 categories in a way according to a uniform distrubution with
either equal proportions for all 12, or even more difficultly 12 non-equal proportions."

The answer is a single real number which should probably be rounded upwards to the nearest whole number above.
(A few rather vague guesses might be: 113, 129, 123 etc., but without more evidence I do not know. Chi-Squared does not
give the correct answer to this because it gives hypothesis analysis treating all 12 categories as potentially biassed and
it could be said that I am considering that either 11 are uniform and 1 is biassed or all 12 are uniform as the null hypothesis
this as I have explained is so ridiculous in real life contexts that I so far cannot think as to why a well designed serious
study should really do this, but an MIT lecture used something similar as a purposefully very bad example of a poor study design
since it "draws a dartboard around the result after the data was collected" or in my words either uses an unjustified unsound SP, or
leaves the statistician with the job of working out a suitable increased level of significance required to make the hypothesis
one which COULD still be rejected, but only if some very remarkable result were obtained where one month were very
unusual indeed. I am trying to formalise my attempt of dividing by 12 (or 24) the significance probability, but intuitively it needs
probably a very complicated adjustment, it is more difficult than I thought, and probably more like dividing SP (0.01) by 132 say.
The SP fudge factor may of course be an irrational number with factorials, square roots and all sorts all over the place.)

I suppose I have been taught the ground work to be able to program a computer to do a simulation, but it is rather
awkward - not something I would want to spend too long on, and not an entirely satisfactory answer even then.
If someone finds things like this easy or has a software package that can solve this in less than
30 minutes work (eg. bobbym perhaps if his software packages are very powerful indeed.)
then it would be interesting to see if you could answer this to help build my intuition.
If a serious course taught how to solve this they would probably want the algebra that proves
and/or illustrates why it works and a numerical answer (eg. 121) would not get any marks.
My intuition is this is of Masters Degree Level, but someone might prove me wrong. (I had intended it to be only A-Level or BSc)

I wonder whether the loaded dice formulas are of any use with this... (Here we go again...)
The problem is rather like trying to prove a matter concerning a 12 sided die by rolling it 1000 times.
I have tried looking at the biassed coin wikipedia page and I cannot really adapt it for this because
that is fine for two states (heads,tails) but not for {1,2,3,4,5,6,7,8,9,10,11,12} - 12 states.
It is at least one level of difficulty above a problem that I found that the wiki site did something
that I did not understand and anonimnystefy did not really give a very full account of, but sounded
like he knew and understood about in the Exercises - Statistics thread some time ago. I can apply the formula,
but do not fully understand the derivation, and this would have to be made even more complex
to solve the full solution to the problem.