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Invisibleonce in a lifetime
sun child
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Re: mathematical brain teaser thread [Re: Sun King]
    #21868109 - 06/28/15 11:28 AM (8 years, 7 months ago)

Rosemary served first; I had to familiarize myself with the rules.

Since the serve alternates between games, one player has 5 serves, the other has 4, out of 9 games. 

Since 5 wins came from the 2nd player serving, the person who won 3 games couldn't have been the 2nd player serving,

Therefore, the winner of the set was the second player to serve,

So Rosemary served first and Miranda second.


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InvisibleDividedQuantumM
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Re: mathematical brain teaser thread [Re: once in a lifetime]
    #21868126 - 06/28/15 11:34 AM (8 years, 7 months ago)

Quote:

once in a lifetime said:
Rosemary served first; I had to familiarize myself with the rules.

Since the serve alternates between games, one player has 5 serves, the other has 4, out of 9 games. 

Since 5 wins came from the 2nd player serving, the person who won 3 games couldn't have been the 2nd player serving,

Therefore, the winner of the set was the second player to serve,

So Rosemary served first and Miranda second.





Sorry, this is incorrect.  Miranda served first.  Before I post the proof, can anyone explain why?


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sun child
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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21868145 - 06/28/15 11:39 AM (8 years, 7 months ago)

Hehe, maybe I should have asked for rule clarification before I went further.

It was my understanding that serve alternated each game, regardless of who won - was this correct?


--------------------
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I Wish You Peace, Lawrence Laughing                                                                                                                    Do Your Thing, Moondog                     
large  . . music garden . .  very
all peace                    them hi
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sun child
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Re: mathematical brain teaser thread [Re: once in a lifetime]
    #21868159 - 06/28/15 11:42 AM (8 years, 7 months ago)

I.e., the person served first would serve 4 times, and return it 5 times - aha, that's what my mistake was.

Okay :smile:

Yep - first player serves first 4 times, and returns the serve 5 times, so the first player had the 5 wins, so the first player had to be Miranda.

.

Don't give me any points though; you had to walk me to it. :smile:


--------------------
Innocent, Oldfield & Hegerland          Julia Delaney, Bothy Band                                        Rasta Girl, Sister Carol                    Genesis, Jorma K
I Wish You Peace, Lawrence Laughing                                                                                                                    Do Your Thing, Moondog                     
large  . . music garden . .  very
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InvisibleDividedQuantumM
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Re: mathematical brain teaser thread [Re: once in a lifetime]
    #21868249 - 06/28/15 12:04 PM (8 years, 7 months ago)

Correct answer:

1  2  3  4  5  6  7  8  9
R M R M R M R M R
R M R M R M M M M
X  X  X  X  X  X    X
                        X        X

Tennis players alternate in serving.  Assume that Rosemary served first.  The set included nine games, so she must also have served last.  Since Miranda won the set, she must have won the last game.  Of the eight games that remain, therefore, five were won by Miranda, three by Rosemary.  Consider the three that Rosemary won.  There are four possibilities:

A. Rosemary served all three.
B. Rosemary served two.
C. Rosemary served one.
D. Rosemary served none.

The chart illustrates the first possibility, with three Rs placed in the third row beneath any three Rs in the second row.  The remaining blanks of the third row must be filled by Ms.  This shows only two games won against service; therefore possibility A is eliminated.  Similar charts eliminate B, C, and D.  This exhausts the four possibilities, proving that Rosemary could not have served first.  By drawing a new chart and following the previous procedure, it will be found that all data can be accounted for on the assumption that Miranda served first and that Rosemary served one of her three winning games.


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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21868284 - 06/28/15 12:10 PM (8 years, 7 months ago)

Please continue. :smile:


--------------------
Innocent, Oldfield & Hegerland          Julia Delaney, Bothy Band                                        Rasta Girl, Sister Carol                    Genesis, Jorma K
I Wish You Peace, Lawrence Laughing                                                                                                                    Do Your Thing, Moondog                     
large  . . music garden . .  very
all peace                    them hi
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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21868305 - 06/28/15 12:14 PM (8 years, 7 months ago)

PROBLEM 6


Quote:

Take the digits in descending order, 9 through 1, and form an expression equal to 100 by inserting the smallest possible number of plus or minus signs.




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InvisibleDisoRDeR
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Re: mathematical brain teaser thread [Re: DividedQuantum] * 1
    #21868782 - 06/28/15 02:17 PM (8 years, 7 months ago)

I'm not sure if this minimizes the plus and minus signs, but the first one I found was

98 - 76 + 54 + 3 + 21 = 100


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Re: mathematical brain teaser thread [Re: DisoRDeR]
    #21869130 - 06/28/15 03:46 PM (8 years, 7 months ago)

Quote:

DisoRDeR said:
I'm not sure if this minimizes the plus and minus signs, but the first one I found was

98 - 76 + 54 + 3 + 21 = 100




:mushroom2::mushroom2::mushroom2:

Correct!


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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869144 - 06/28/15 03:49 PM (8 years, 7 months ago)

PROBLEM 7


Quote:

"The number of words in this sentence is nine."  The sentence just quoted is obviously true.  The opposite of a true statement is usually false.  Give a sentence that says the exact opposite of the quoted sentence but is nevertheless true.




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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869180 - 06/28/15 03:58 PM (8 years, 7 months ago)

There is no such thing as an opposite to a sentence.


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Re: mathematical brain teaser thread [Re: OrgoneConclusion]
    #21869234 - 06/28/15 04:14 PM (8 years, 7 months ago)

That's not what I was looking for.


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InvisibleOrgoneConclusion
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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869243 - 06/28/15 04:16 PM (8 years, 7 months ago)

Nevertheless, your puzzle is nonsensical. Try rephrasing.


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InvisibleKurt
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Re: mathematical brain teaser thread [Re: OrgoneConclusion]
    #21869247 - 06/28/15 04:17 PM (8 years, 7 months ago)

I agree with OC, technically. Truth value is not in what we say but show (like in truth tables of logic textbooks). But I don't think this is a "logical" problem in that sense, is it?

As a matter of speaking:

"The number of words in this sentence is not nine."


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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869252 - 06/28/15 04:18 PM (8 years, 7 months ago)

"The number of words in this sentence is nine, not."


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Re: mathematical brain teaser thread [Re: Kurt]
    #21869253 - 06/28/15 04:18 PM (8 years, 7 months ago)

Quote:

Kurt said:
I agree with OC, technically. Truth value is not in what we say but show (like in truth tables of logic textbooks). But I don't think this is a logical problem is it?

As a matter of speaking:

"The number of words in this sentence is not nine."





:mushroom2::mushroom2::mushroom2:

Correct!


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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869258 - 06/28/15 04:20 PM (8 years, 7 months ago)

What is the opposite of 'the'?


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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869270 - 06/28/15 04:24 PM (8 years, 7 months ago)

PROBLEM 8


Quote:

A group of airplanes is based on a small island.  Each plane's tank holds just enough fuel to take it halfway around the world.  Any desired amount of fuel can be transferred from the tank of one plane to the tank of another while the planes are in flight.  The only source of fuel is on the island, and for the purposes of this problem it is assumed that there is no time lost in refueling either in the air or on the ground.  What is the smallest number of planes that will ensure the flight of one plane around the world on a great circle, assuming that the planes have the same constant ground speed and rate of fuel consumption and that all planes return safely to their island base?




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Re: mathematical brain teaser thread [Re: OrgoneConclusion]
    #21869278 - 06/28/15 04:26 PM (8 years, 7 months ago)

Quote:

OrgoneConclusion said:
There is no such thing as an opposite to a sentence.




By the way the problem says

Quote:

Give a sentence that says the exact opposite




says the exact opposite, not is the exact opposite.

There is nothing wrong here.

What a pointless aside.


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InvisibleOrgoneConclusion
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Re: mathematical brain teaser thread [Re: DividedQuantum]
    #21869290 - 06/28/15 04:29 PM (8 years, 7 months ago)

Quote:

says the exact opposite, not is the exact opposite.





:badsurprise:

Huh?


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