Math Is Fun Forum

I was hoping for this method:

(1) First divide the total of £400 into 5 equal parts. £400 / 5 = £80
(2) Then give 3 of them to Lisa: £80 x 3 = £240

That was one to try I can make up a few more a bit later and send them by email.

It might be best to think of it purely in GMT converting the defined start time into GMT start time for the 2013 Easter.
I would not swear to this as correct, but personally I think that the mid-point is the 10th October at 30 minutes past midnight,
that is after conversion back to BST which is the correct format of the time zone on the 10th October. (???)
In GMT 11:30pm on the 9th October if we were in GMT which the UK wasn't on that date of course.
It's a good job I didn't involve any space time distortion physics really !! That would have been really difficult !!
Joking aside I was thinking of making up an example of someone doind a mid point between two countries with
two time zones, but the same sort of event in 2 years... Anyway I can't think of another dec / oct thing apart from
my observation that:

10 in decimal = 8 + 2 = 8 is 10 in oct and 2 units = 12

So convert using the function of decimal into base 8 and the month of October nicely converts into a "12".
This is the inverted way round to the original joke of: 31 Oct = 25 Dec
so it does not quite work.

I am getting 9th and 10th of October 2013 for the mid-point. (ie: midnight after the 9th October)

Okay how about this one:

Does British Summer Time (BST) and Greenwich Mean Time (GMT) considerations make any difference to the
exact mid-point between the end of Easter Sunday of 31st March 2013 (BST) and midnight immediately before
the start of 20th April 2014 in which we are in GMT technically ?

Start of BST in 2013: Early hours of 31st March 2013 (clocks go forward one hour)
End of BST in 2013: Early hours of 27th October 2013 (clocks go back one hour)

Start of BST in 2014: Early hours of 20th April 2014 (clocks go forward one hour)

Do we have to add half an hour, subtract half an hour, or is there no change, or is there a different adjustment ?

That is fine by me.

I was hoping when I wrote that that the two lengths would be near to being equal, but they are not that close in fact:

(1) 31st March 2013 to 31 October 2013. How many days is that ?
(2) 31st October 2013 to 20th April 2014. How many days is that ?

To be frank the only difficult thing about my puzzle is that silly mistakes and off by one errors are very easily
made with those. A computer programmers puzzle might be to write some code that can solve things like that....
Anyway according to my reckoning.... (well I won't tell you the answer, but it wasn't as close as I had thought).

Happy Easter.

I have not read the article, but this is what I reckon: [Sorry about the contraversial comments here but....]

It was probably motivatated by a left wing minded thinker who has an atheistically based criticism of both the
belief in god, belief in Bible stories and of course divine rights to rule used as an excuse for, in effect, a dictatorship
through a very long period of history, finally stopped of course in the modern age thankfully by democratic voting,
fair systems for things, good government, much better communication (internet very recently, newspapers, magazines,
TV, radio, books, schools, other education) making us wiser and less likely to believe in tall stories about things.

I do as a personal view agree that such stories are probably rather 'fantastic' stories reflecting the triumph of good
against evil rather like a film does nowadays, but we are all human and all entitled to out beliefs. The only trouble
is that most of our laws are based on the teachings of scriptures in a way: modern versions of the same philosophy,
and it so happens that I believe in the philosophy but not the god.

Another point: If the metaphor Jesus gave about rich people not being able to go to heaven was right, then
the scholar cannot be very wise to the Bible. If the rich are encouraged not to get rich, or to give it to charity,
then this would have helped the poor as would numerous other things that it taught. Once again I agree with
the philosophy, but not the justification. It should be done because it is right, not in a dream of going to heaven.

Maths problems where the logic of the question is difficult to understand are very confusing. They are more like an English
comprehension problem than a Maths problem. Either it is deliberate in which case it reads like a brain teaser or mensa challenge,
or unintended, in which case the problem needs to be written more clearly perhaps with a word they forgot to mention or something.

Anyway hi everyone. Welcome to the forum

Maybe you should use the fact that (1/n) is one of the terms of the product and all of the others are one or less.
Then use the fact that if you multiply by a number between zero and one it reduces a positive number or keeps
it the same when it is equal to one.
Then I think you can make Bob's deduction.
In a formal proof that needs to be written out correctly. If you are doing a pure maths related course, then I
should do the rest as an exercise, mukesh, if you just copy someone else's version then you won't understand it.
anonimystefy: I agree. Strictly speaking in a formal proof that probably isn't enough. Suppose the product sequence
converges to one with increasing density, as n inreases, all near to one. The product could converge to a higher number.

Hi bobbym and Mandy,

I was a bit slow with my reply Mandy, but I have sent two emails now about this and I think
you have made the right choice if I am right in thinking that you are not going to the college
course and instead making good use of your current materials.
(Let me know if I have got that wrong.)

At the end of the day everyone has to make their own choices, but advice does help people
and everyone will have their own opinion on these things.

The college to which you refer teaches A Levels and other things, but does do some GCSEs.
The level of Everyday Maths which you are finding difficult is actually below GCSE level.
So therefore it would be a struggle, but at the end of the day I don't know all the facts and
have little to go on. College course do have many advantages including good skills of teachers
that help motivate, teach, and train students, but the course level is the same level in theory
regardless of the learning college or open learning company you choose.

However this website has been very useful to me, and to many others, so do carry on this
thread Mandy and good luck with your learning.

Stephen

For the somewhat easier question (2) my answer is:

December has 31 days, January has 31 days, February has 28 days (assuming the study is done on a non leap year).

31 + 31 + 28 = 90 days in winter period as defined in the question

365 - 90 = 275 days in non winter period

Let the sample size be n = 1000

mean in winter period using binomial model = np = (90/365) x 1000 = 246.57....

variance using binomial model = npq = (90/365) x (275/365) x 1000 = 185.775....

standard deviation = 13.62996....

Use normal approximation with 2.33 standard devations from the mean for 1% siginificance test, one tailed:
2.33 x 13.62996.... + 246.57.... = 278.3331....
Using rounding up to allow a little extra 279 would be my answer (using the normal approximation) to question 2.
So at least 279 cases of catching a cold in winter out of 1000 cases of catching a cold would give strong evidence
in a one tailed scientific study.
In practice the scientist would probably want to log every exact date combined with the recent weather conditions of each,
including maximum and minimum temperature of recent days prior to catching a cold, then do some sort of regression analysis of
temperature against the number of cold cases per unit of time. Exactly how to do a hypothesis test for this data I am not
sure at the moment. I think something similar did get taught in my course in 2006, but I cannot remember the details at present.
I have lost some of my notes and materials, but do still have the textbook that came with the course.
A scattergraph would probably show an interesting picture, but how to formalize it I am not sure. I think it was made easy
with some software which avoided the need for hand calculations.