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#27021 - Wed May 08 2002 12:02 AM The Sunday Times .. Brain Teaser XI
gtho4 Offline
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Registered: Sun Dec 26 1999
Posts: 51328
Loc: Sydney
oz downunder
The Deflating Mangoes
quote:
The Lotaseetas have a rather casual attitude to commerce. Every Monday morning, Ming, the rice-planter, gathers from the grove outside his bungalow a number of mangoes of uniform weight. For the rest of the week he uses these as weights for measuring out the rice on his scales, charging each customer according to the number of mangoes required to balance the weight purchased.

Unfortunately, the mangoes themselves lose a fixed percentage of their weight each day by evaporation. However, Ming roughly compensates for this by using two mangoes as the unit on Wednesdays and Thursdays and three mangoes on Fridays. Clearly, Wednesday is a good day for buying rice and Tuesday is a bad day.

His first customer at precisely 10 o'clock each morning (they are late risers) is Fung, the rice merchant, who always buys the same quantity of rice for his shop. On Monday Fung's rice cost him 243 cowries. On Friday it cost him 256 cowries.

How much did it cost him on Tuesday?


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#27022 - Thu May 09 2002 11:28 PM Re: The Sunday Times .. Brain Teaser XI
sean5789 Offline
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Registered: Sun Apr 28 2002
Posts: 35
Loc: Orland Park Illinois USA    
I gave the math a try, but I am still stuck with two variables and one equation. Will give it another try a little later.

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#27023 - Thu May 09 2002 11:33 PM Re: The Sunday Times .. Brain Teaser XI
sean5789 Offline
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Registered: Sun Apr 28 2002
Posts: 35
Loc: Orland Park Illinois USA    
I played with the math and got 164.167 or 164 1/6. Close at all?

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#27024 - Fri May 10 2002 01:00 PM Re: The Sunday Times .. Brain Teaser XI
gtho4 Offline
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Registered: Sun Dec 26 1999
Posts: 51328
Loc: Sydney
oz downunder
the answer is a whole number
curiously, it's around twice the value of what you've posted

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#27025 - Fri May 10 2002 02:45 PM Re: The Sunday Times .. Brain Teaser XI
sean5789 Offline
Participant

Registered: Sun Apr 28 2002
Posts: 35
Loc: Orland Park Illinois USA    
Okay, I had a plus sign that should have been a minus sign.

Is it 322 cowries?

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#27026 - Fri May 10 2002 03:19 PM Re: The Sunday Times .. Brain Teaser XI
gtho4 Offline
Administrator

Registered: Sun Dec 26 1999
Posts: 51328
Loc: Sydney
oz downunder
warmer!

the answer's in the 320s

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#27027 - Sat Jun 08 2002 12:55 AM Re: The Sunday Times .. Brain Teaser XI
gtho4 Offline
Administrator

Registered: Sun Dec 26 1999
Posts: 51328
Loc: Sydney
oz downunder
that's a gimme

the answer is 324

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#27028 - Sat Jun 08 2002 03:27 AM Re: The Sunday Times .. Brain Teaser XI
lbruggem Offline
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Registered: Tue Apr 16 2002
Posts: 417
Loc: The Netherlands
Could you perhaps explain the answer?? Have been thinking about this one for quite some time, but no way I could solve it... [Big Grin]
_________________________
----------------------- Errare humanum est, perseverarum diabolicum - Marcus Tulius Cicero

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#27029 - Sat Jun 08 2002 07:36 PM Re: The Sunday Times .. Brain Teaser XI
gtho4 Offline
Administrator

Registered: Sun Dec 26 1999
Posts: 51328
Loc: Sydney
oz downunder
hope you can read this, as keyboards and formulae aren't that friendly

taking the weight of one mango on Monday as W units, on Tuesday as We, on Wednesday as We2, on Thursday We3 and on Friday as We4, then the cost of the quantity of rice R is:

[ e is less than one as the weight of the mangoes falls each day by evaporation, and is a constant ]
[ 2 means squared, 3 mean cubed etc. ]

Monday: R/W currency units [ 243 ]
Tuesday: R/We currency units
Wednesday: R/2We2 currency units
Thursday: R/2We3 currency units
Friday: R/3We4 currrency units [ 256 ]

thus: Monday/Friday = (R/w)/(r/3We4) = 3e4 = 243/256
and further elimination of 'common factors' gives: e4=81/256
which itself gives: e=3/4
[ e equals three-quarters ]

and therefore Tuesday's cost: (Monday's cost)/e = 243/(3/4) = 324

the daily costs were:
Monday 243
Tuesday 324
Wednesday 216
Thursday 288
Friday 256

anyone know how to write e squared on a keyboard?
e2

[ June 08, 2002, 08:41 PM: Message edited by: gtho4 ]

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#27030 - Sun Jun 09 2002 11:52 PM Re: The Sunday Times .. Brain Teaser XI
lbruggem Offline
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Registered: Tue Apr 16 2002
Posts: 417
Loc: The Netherlands
Thanks George! I could read it perfectly well, even with the missing superscripts! [Big Grin] I have no clue how to make them. Copying from Word doesn't work... [Frown]
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----------------------- Errare humanum est, perseverarum diabolicum - Marcus Tulius Cicero

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