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Numbered spoons


Best Answer nakulendu, 14 March 2013 - 10:10 AM

Spoiler for Spoonfeeding - at least one way

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#1 bonanova

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Posted 14 March 2013 - 06:02 AM

OK so there is this black velvet bag that contains a bunch of uniquely numbered balls spoons.

Every puzzle has numbered balls. Enough with the balls. This puzzle has spoons.

 

You will be asked two questions about these spoons.

 

In order to get the needed information I ask my beautiful assistant here [pic load failed; sorry ^_^ ]

to remove from the bag some quantity of spoons, add their numbers and write it on a sheet of paper.

She looks at you, smiles, and suggests that should be enough information for you.

 

You disagree and ask her to replace the spoons and repeat the process, which she does,

drawing the same number of spoons from the bag but this time the sum she writes is a different number.

You ask her to do it again. And again, ... until the sums begin to repeat themselves, and eventually

you are convinced that no more new numbers will appear.

 

She then erases any duplicates, keeping only one occurrence of each, and hands you the paper.

On it you see:

 

115  118  113  110  120  117  116  112  121  114

 

Then you are asked:

How many spoons are in the bag, and what are their numbers?

 

You think for only a moment and say that you need more information,

like how many spoons were drawn each time.

 

My smiling assistant says she can't tell you that; but she can tell you that the sum of the number

of spoons in the bag and the number of spoons drawn each time is an odd number.

 

You pull out a used envelope, turn it over [everyone does this], scribble something,

and then give your answer.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 Krishna Kutty

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Posted 14 March 2013 - 08:33 AM

Good going with the spoons! :thumbsup:


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#3 nakulendu

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Posted 14 March 2013 - 10:10 AM   Best Answer

Spoiler for Spoonfeeding - at least one way


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#4 bonanova

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Posted 14 March 2013 - 03:08 PM

Spoiler for Spoonfeeding - at least one way

 

Very nice.!

 

Spoiler for With regard to duplicates


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#5 googon97

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Posted 14 March 2013 - 04:19 PM

Spoiler for easiest answer in my opinion


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#6 bonanova

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Posted 14 March 2013 - 04:25 PM

Spoiler for easiest answer in my opinion

 

Very nice, and I thought you had me on that point.

But I read the OP again, and sure enough, it says ...

 

You disagree and ask her to replace the spoons and repeat the process,

 

But you get honorable mention anyway. Your solution works except for the red letter.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#7 googon97

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Posted 14 March 2013 - 08:00 PM

I do agree it does say spoons.

Spoiler for easiest answer in my opinion

 

Very nice, and I thought you had me on that point.

But I read the OP again, and sure enough, it says ...

 

You disagree and ask her to replace the spoons and repeat the process,

 

But you get honorable mention anyway. Your solution works except for the red letter.

However, if you didn't know how many spoons were taken, would you ask please replace the spoon?


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#8 bonanova

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Posted 15 March 2013 - 05:43 AM

I do agree it does say spoons.

 




Spoiler for easiest answer in my opinion

 Very nice, and I thought you had me on that point.But I read the OP again, and sure enough, it says ... You disagree and ask her to replace the spoons and repeat the process, But you get honorable mention anyway. Your solution works except for the red letter.
However, if you didn't know how many spoons were taken, would you ask please replace the spoon?

The question of implication is an interesting one.

A previous Forum discussion centered on whether the statement "All my cars are Fords" implied that I had at least one car, and that it was a Ford. What do you think? My take was that it meant "For any object that is a car and that I own, that object is also a Ford." There may not be any such objects, but the statement nonetheless has meaning: If there is such an object then that object is a ford. The premise does not have to be true on a conditional.

The discussion continued until I said that I once saw an empty field that bore a sign "All trespassers will be prosecuted." The sign was meaningful even tho the field clearly was empty. That is, the sign did not imply the existence of at least one trespasser.

I'll concede your point as it applies to "some number of spoons." That number clearly could be one. Or zero, for that matter. But if she had drawn just one spoon, I could not say "replace the spoons". I would have to say "replace all the spoons that you drew." Well, that is the appropriate statement to have  made, I guess. I didn't know the number; the OP simply presupposes that I knew is was plural.

 

So your point is better taken than I first thought. Let's say, though, that had she drawn only one spoon, then to be responsive to what I asked, she would have to have said "I can't do as you ask." or "I don't understand what you are referring to." or something other than just doing the replacement. In that sense, the OP (by careful reading, and way too much over-thinking) rules out the one-spoon case. Kind of.

In any case it was only a fortuitous accident that the OP covered the case of one spoon at all. I'm not clever enough to have done that by plan. I simply didn't think of the case.

Good solve!


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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