A Fistful of Brain Teasers

What would be the annual percentage rate for the 2018 global population of 7.6bn to reach 10bn by 2038 ?

Assume the annual percentage growth rate is the same for every year for the next 20 years.

3 decimal places will be enough.

Bruce has volunteered to mow the Yorkshire Dales No.1 village cricket ground. He has a tractor-mower that cuts a strip that is 2 metres wide.

The ground is circular with a circumference of 400 metres. He starts from the outside of the ground and goes around in ever-decreasing circles towards the centre.

Estimate the total distance he has travelled on his journey to the centre. You can ignore the inevitable “wiggles” he must make at the end of each circular transit.

A starter........................

"bn" means Billion, nothing to do with the "unknown" which I have called "n"

PS. don't be put off by the large white space beneath the two starter lines. I only used about another five lines and that was just to make every step crystal clear !

1.382% based on Excel's ability to calculate roots.

As you shown, of the current level is 7.6bn and the gross rate of growth is n, then to reach 10bn in 20 years the calculation is 7.6bn * n^20 = 10bn.

So resolving, n^20 = 10bn/7.7bn = 10/7.6 = 1.316

So n = 20th root of 1.316, Excel tells me that is 1.013816, which is a percentage growth rate of 1.382% to 3dp.

Eoink posted:

1.382% based on Excel's ability to calculate roots.

 

As you shown, of the current level is 7.6bn and the gross rate of growth is n, then to reach 10bn in 20 years the calculation is 7.6bn * n^20 = 10bn.

So resolving, n^20 = 10bn/7.7bn = 10/7.6 = 1.316

 

So n = 20th root of 1.316, Excel tells me that is 1.013816, which is a percentage growth rate of 1.382% to 3dp.

Yes ! Excel is a very powerful tool. I don't think most users are aware of even half of its capability !

Well done, BTW !

For the benefit of the "more mature" members of the forum, the above process might bring back happy memories where those six-figure Log Tables came in handy !!

Time !

I went to a meeting on Tuesday evening and listened to two sides of an argument. It was a very well organised meeting and very civil, each speaker being heartily applauded by all those present.

The lead speaker from each side was allocated 10 minutes in which to present their case. Each side supported its case with 4 supplementary speakers, each allocated 4 minutes per speaker.

The assembled Members of this organisation were then invited to speak (in they so wished) for a maximum of two  minutes per speaker.

Now one such member complained that the allocated time for members was inadequate. But he used the phrase " Mr. President, two minutes aren't adequate for me to present my point of view"

I thought he should have used the phrase "Mr. President, two minutes isn't adequate for me to present my point of view"

So my question is ...is an allocation of time (eg 2 minutes; 4 minutes etc) singular or plural. Or does it not matter ?

PS I don't know the answer, but i hope somebody here does ! Just to put my tiny mind at rest !!

Don Atkinson posted:

Time !

I went to a meeting on Tuesday evening and listened to two sides of an argument. It was a very well organised meeting and very civil, each speaker being heartily applauded by all those present.

The lead speaker from each side was allocated 10 minutes in which to present their case. Each side supported its case with 4 supplementary speakers, each allocated 4 minutes per speaker.

The assembled Members of this organisation were then invited to speak (in they so wished) for a maximum of two  minutes per speaker.

Now one such member complained that the allocated time for members was inadequate. But he used the phrase " Mr. President, two minutes aren't adequate for me to present my point of view"

I thought he should have used the phrase "Mr. President, two minutes isn't adequate for me to present my point of view"

So my question is ...is an allocation of time (eg 2 minutes; 4 minutes etc) singular or plural. Or does it not matter ?

PS I don't know the answer, but i hope somebody here does ! Just to put my tiny mind at rest !!

I would say either is correct because it depends on what is meant.  If you he is saying that two minutes, as opposed to three or four or whatever, then "aren't" would be correct - in the same way that 2 ducks are not enough (ducks) for a dinner for 5 people.  And in the same vein you could say "1 minute isn't enough...". But if you are thinking of a duration of time, then "isn't" would be correct - "5 minutes isn't enough (time)"

So you can think of it as "5 minutes aren't enough (minutes) " or "5 minutes isn't enough (time)".

IMV

“Two minutes” is plural, and so “two minutes aren’t enough” is correct. The alternative would be to say “a time slot of two minutes isn’t enough”, singular because the subject of the sentence is “a time slot”, the two minutes being an adjectival phrase describing the slot.

In most circumstances, the correct form would be 'two minutes isn't enough' because you're really thinking of a period of two minutes - not two minutes, taken separately. The same applies to distances: 'five miles is a long distance'.

SamClaus posted:

In most circumstances, the correct form would be 'two minutes isn't enough' because you're really thinking of a period of two minutes - not two minutes, taken separately. The same applies to distances: 'five miles is a long distance'.

You can indeed say “ Two minutes isn’t adequate” because the there is an understood subject, time, so the sentence in effect reads: “Two minutes isn’t adequate [time]”.

But the original sentence confuses this by going on, which would have to read “Two minutes isn’t adequate [time] for me to present my point of view.” In the context of the full sentence I don’t think it works with “time” having to be clearly inderstood by both speaker and listener, so in my view the sentence reverts to “two minutes” being the subject, which as I said in my last post  is plural, so I still believe “aren’t” is correct.

N.B.My previous post incorrectly substituted “enough” for “adequate”, but that does not alter what I said. 

But a minute in itself cannot be 'adequate' or 'inadequate' - 'adequate' for what?

The writer is necessarily referring to a period of time of two minutes. Hence the singular...

An interesting exchange, which illustrates the flexibility of English.

Adequate for what has been defined: the rest of the sentence was “...adequate for me to present my point of view”.

I think the primary debate is whether [time] is so clearly the subject, rather than “two minutes” that it inevitably is a missing word understood by all parties. Just as in the sentence “Please make a cup of tea”, which has an understood “you” or a person’s name “[You] make a cup of tea.” Or [Don] make a cup of tea“. It doesn’t work if ambiguous, with more than one person is present as they don’t know to whom it is aimed, and so in this case, the listener doesn’t know.

looking at it another way, is the person saying that a particular number of minutes is not adequate, with focus on the number, or are they saying that the time slot they have been given is not adequate, focus on it being too small a fixed length slot.

In conclusion perhaps indeed both are correct, the speaker himself defining what the focus is on, bupy whether he says isn’t or aren’t...

And as the speaker did make the choice, Don was wrong in not recognising tbat the focus was the number of minutes.

Hmmm....

Just as in the sentence “Please make a cup of tea”, which has an understood “you” or a person’s name “[You] make a cup of tea.”

This is known as the imperative - there's no word missing, it's not an elliptical form.

"Kiss me" is another example of the imperative - but you needn't take it literally if you don't feel like it at that precise moment...

The more I think about it - and BTW, many thanks for all the contributions - the more i'm convinced the "two minutes" is a singular.

Each speaker was allocated a "block of time" The size of this block was defined in minutes. But it could have been 120 seconds, or 1/30th of an hour, or "until the bell rings". (in fact a little bell was actually used to mark the end of each time-block and every speaker who used the full 2 minutes, wound up their speech within a few seconds of hearing the bell !)

So, whilst not absolutely convinced in my own mind, i'm inclined towards the "singular" point of view.

My eldest son-in-law is called Christopher. Ok, we all call him Chris.

He has quite a nice family truck, you know, the sort with a massive cab, two rows of seats - full-size - not one of those with cramped rear seats for dogs !

Now if I refer to Christopher's truck, I hope we all agree that i've got the apostrophe in the right place.

But if I use his normal name, Chris, what do I do about "s"s and apostrophes ?

Chris' truck.

Don Atkinson posted:

But if I use his normal name, Chris, what do I do about "s"s and apostrophes ?

Usually people would write Chris’ Truck, however Chris’s Truck is not wrong.  The latter being how you would pronouns the sentence 

Found on another website:

In fact, both forms are acceptable. For example, the Modern Language Association recommends adding an 's' after the apostrophe, while the Chicago Manual of Style allows omitting the 's' as an alternative practice. The exact conditions under which the respective methods are preferred are likely subjective. As a general rule, it is suggested that the 's' be omitted if it makes it awkward to pronounce, like in Moses' or Socrates'

which ties in with what Eloise said above.

The OED concurs with the above but also notes some exceptions for organisations or establishments, such as St. Thomas’ Hospital.

Personally speaking (as the other Christopher M on this forum, and also a long suffering supporter of The Saints ), it has always been “Chris’s” around my friends & family.

Chris's is the grammatically correct form - Chris' is generally acceptable (and is the normal form in the US). Same with Prince Charles's/ Prince Charles', etc.

I was wrong and take back with embarrassment what I said in my earlier post, now deleted.

Apostrophe with no additional s if the word ending in s is pleural, e.g peoples’, but s after the apostrophe when it is simply a word ending in s, as in this case, so Chris’s. And it is not optional, at least in British English.

There is of course always the debate as to what is correct when language changes through misuse, as historically it always has, though my view is that other than new words it is, or should be, more fixed now as everything is well documented and most people brought up in Britain have had at least a basic opportunity for education in the language. I.e. we do not have to accept Americanisms, though they do creep in through the near universal dominance of the USA in films and many TV shows and computer games etc, often the prime source of vocabulary for young people in particular.

An easy one !

If X + Y = 16 and X*Y = 55 what are the values of X and Y

PS when I saw this on another website, I thought "there's got to be more to this than meets the eye.....there wasn't"

11 and 5?

Yep 11 x 5

I disagree: definitely x=5 and Y=11