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deadkenny
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Topic: The Grey Cells - Exercise ! Posted: 31-Jul-2008 at 18:05 |
Waiting for you question gcle - the 'price' for showing everyone how smart you are.
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"Those who cannot remember the past are condemned to repeat it." George Santayana
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gcle2003
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Posted: 31-Jul-2008 at 18:37 |
Sorry, I'd forgotten about that.
Here's one from Martin Gardner:
A commuter is in the habit of arriving at his suburban station each evening exactly at 5 o'clock. His wife always meets the train and drives him home. One day he takes an earlier train, arriving at the station at four. It's a nice day, so instead of waiting for his wife he decides to walk towards home, using the route his wife takes. They meet somewhere on the way. He gets in the car and they drive home, arriving there ten minutes earlier than usual. Assuming she always drives at a constant speed, and that on this occasion she left just in time to meet the five o'clock train when it arrived, can you say how long the husband walked before he was picked up? (By his wife, that is )
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deadkenny
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Posted: 01-Aug-2008 at 15:30 |
Originally posted by gcle2003
..., can you say how long the husband walked before he was picked up? (By his wife, that is ) |
One hour.
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"Those who cannot remember the past are condemned to repeat it." George Santayana
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gcle2003
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Posted: 01-Aug-2008 at 18:17 |
Can we have some reasoning? It's not the approved answer.
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Northman
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Posted: 01-Aug-2008 at 20:09 |
I'd say no - we cannot determine how long he walked.
We only have a timedifference between the two trains, and the 10 minutes timedifference for arriving home. We need at least one information/relation more, ie. the time it takes to drive to the station or exact speed or something.
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gcle2003
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Posted: 01-Aug-2008 at 20:29 |
I'll give it another 24 hours?
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Northman
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Posted: 01-Aug-2008 at 20:31 |
Originally posted by gcle2003
I'll give it another 24 hours? |
But no further information I take it
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Northman
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Posted: 01-Aug-2008 at 23:25 |
I just realised I might have misunderstood the question, and knowing you gcle, it can only be due to my inadequate command of english.
When you ask "how long the husband walked" - that means a distance to me, like "hvor langt manden gik" in danish.
But if the same can mean "for how long (time) the husband walked" - then of course, you are asking about a period of time, and that makes it somewhat easier.
How's this: They get home 10 minutes earlier than usual - meaning the total driving time for the wife is 10 minutes less than usual, 5 minutes in each direction.
Then she must have picked him up 5 minutes earlier than the usual 5 o'clock. She has already earned the first 5 minutes out of the 10 minutes saved, in order to reach him. So she picked him up at 4:55 and as he got off the train at 4:00, he must have walked for 55 minutes.
Edited by Northman - 01-Aug-2008 at 23:30
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deadkenny
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Posted: 02-Aug-2008 at 02:32 |
In writing out my 'solution' I realize that I had made an error, the corrected version confirms Northman's response.
The wife's 'regular' round trip from home to train station and back home takes a length of time equal to T0
The wife's abbreviated trip on the day in question (to 'pick up' point and home) takes time T 1
The husband's walk takes T 2
Now we know that the wife left the house at the usual time, and arrived home 10 minutes earlier than usual. So therefore we know that T 1=T0-10 (the husband's walk 'saved' her 10 minutes).
We know that in total (walk and abbreviated drive combined) the husband's trip from the train station home took 50 minutes longer than normal (he started from the station one hour early, but arrived home only 10 minutes early). So therefore we know that .5*T 1+T2=.5*T0+50
Substituting in the first equation into the second we obtain the following:
.5*(T 0-10)+T2=.5*T0+50
which yields the result T 2=55
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gcle2003
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Posted: 02-Aug-2008 at 11:46 |
Bingo for both of you. I don't know who gets to share the prize.
Northman, in English if I want to know the distance someone walked I would say 'how far did he walk' not 'how long'.
It's an interesting point though. I would say 'how long is this string' looking for a distance. I'm having to think hard to formulate a rule for when to say 'how far' and when 'how long'.
How far is it to New York from Luxembourg? About 3,000 miles.
How long is it to New York from Luxembourg? About 7 hours.
Edited by gcle2003 - 02-Aug-2008 at 11:51
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deadkenny
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Posted: 02-Aug-2008 at 12:09 |
Northman got the correct answer first - so the 'prize' is all his.
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"Those who cannot remember the past are condemned to repeat it." George Santayana
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deadkenny
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Posted: 02-Aug-2008 at 12:19 |
Originally posted by gcle2003
I'm having to think hard to formulate a rule for when to say 'how far' and when 'how long'.
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Being English, it is of course ambiguous in certain situations. The 'rule' though would be something like 'how far' when it is a distance travelled, or the distance between two places. 'How long' would be used for an object, in terms of a 'distance' measurement such as metres. 'How long' would implicitly mean time if it was something that were doing, such as travelling. Thus the question 'How long was your vacation?' would typically mean the length of time for your vacation not the distance travelled on your vacation. (does this count as a 'challenge'? )
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"Those who cannot remember the past are condemned to repeat it." George Santayana
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Northman
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Posted: 02-Aug-2008 at 12:47 |
I am in no position to discuss the finer nuances of english - and of course I'm familiar with the term "far" - like in far, far away.
But until now, I definately would have put it "for how long" - in contrast to "how long" - but it seems like neither of you would consider to use that expression.
Thank you both for adding to my education
Ok - Here is a simple match riddle - grab a matchbox and get thinking, math wont help you a whole lot.
Edited by Northman - 02-Aug-2008 at 15:13
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Zagros
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Posted: 02-Aug-2008 at 13:06 |
I have a whole book full of GMAT questions, if anyone's interested :)
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Zagros
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Posted: 02-Aug-2008 at 13:09 |
Originally posted by Northman
I am in no position to discuss the finer nuances of english - and of course I'm familiar with the term "far" - like in far, far away.
But until now, I definately would have put it "for how long" - in contrast to "how long" - but it seems like neither of you would consider to use that expression.
Thank you both for adding to my education
Ok - Here is a simple match riddle - grab a matchbox and get thinking, math wont help you a whole lot.
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A pyramid? with a base of 4 square and a stick from each corner rising to the centre?
/north: Changed picture
Edited by Northman - 02-Aug-2008 at 15:21
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Northman
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Posted: 02-Aug-2008 at 13:24 |
No Zagros - the entire length of each match must be used and must lie on the periphery of the polygon.
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deadkenny
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Posted: 02-Aug-2008 at 14:57 |
Originally posted by Northman
I am in no position to discuss the finer nuances of english - and of course I'm familiar with the term "far" - like in far, far away.
But until now, I definately would have put it "for how long" - in contrast to "how long" - but it seems like neither of you would consider to use that expression.
Thank you both for adding to my education |
There is formal, technically grammatically correct English, and then there is the language that is spoken. You are correct in terms of the formal usage. However, spoken English is full of instances of 'short cuts' which are commonly used although perhaps not technically correct. So consider the 'lesson' applicable to 'spoken English' only.
Originally posted by Northman
Ok - Here is a simple match riddle - grab a matchbox and get thinking, math wont help you a whole lot.
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Not sure what's meant by 'size' here. Is that area? If so, I can see that the square is 9 (3x3) but isn't the other 5 not 6?
/north: changed picture
Edited by Northman - 02-Aug-2008 at 15:24
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"Those who cannot remember the past are condemned to repeat it." George Santayana
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Northman
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Posted: 02-Aug-2008 at 15:18 |
You are so right deadkenny - a bad typo - I have corrected the number from 6 to 5 in my post - so sorry.
and yes - size is area.
And I'm asking for a polygon the same size as a 2x2 matches - but using all 12 matches.
Added:
All 3 images above are now correct.
Edited by Northman - 02-Aug-2008 at 15:25
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gcle2003
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Posted: 02-Aug-2008 at 16:11 |
I guess one would also say 'how long were you walking for?' but that runs into the rule that you shouldn't end a sentence with a preposition - something that Churchill derided as something up with which he would not put.
'For how long were you walking?' is what you'd expect on an official questionnaire.
Back to the matches....
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deadkenny
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Posted: 03-Aug-2008 at 13:33 |
All I can come up with as a solution is a parallelogram, constructed with long sides of 4, short sides of 2 and with an angle of 30 degrees which gives a 'height' of 1 (see diagram). That gives an area of 4 (base x height = 4 x 1 = 4).
I proposed this solution in a PM, however, Northman suggested that there was a more 'intuitively obvious' solution. By that I assumed that the match sticks would be arranged at right angles or parallel to one another so that one could 'see' the four 'squares' making up the total area (as one can see the five in the righthand figure originally posted). However, I can not see how, as the smallest area I can see being contained by the 12 match sticks, given the additional constraints is 5 - i.e. a 1 x 5 rectangle, or other forms topologically equivalent to it. So I provide my solution, however, I will concede to anyone who can construct such a polygon with area 4, as I have described with the additional constraints.
p.s. I'm not sure how to post an image that I have 'constructed' myself, but is not on a website.
Edited by deadkenny - 03-Aug-2008 at 13:35
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"Those who cannot remember the past are condemned to repeat it." George Santayana
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