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Posted on 2003-03-20
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There is a row of ten boxes and each box contains one object, which is a knife, a fork or a spoon. There is at least one of each utensil. Here are five true statements to help you work out how many of each there are.

: A knife is in more boxes than a spoon is in.
: A spoon is in more boxes than a fork is in.
: A knife is not in precisely five boxes.
: A spoon is not in precisely three boxes.
: A fork is not in precisely half the number of boxes a spoon is in.

How many of each utensil are there?
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Question by:skelmoogies
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Expert Comment

ID: 8177376
I think one of the statements is false.
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Expert Comment

ID: 8177439
x: #knives y: #spoons z: #forks, x > y > z and x+y+z = 10.
y != 3 (given) and y != 4 since (x,z) would then have to be (5,1), so y = 2. Then (x,z) = (7,1) which is then z = y/2? there is no solution for (x,y,z).
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Expert Comment

ID: 8179445
X = Knife, Y = Fork, Z = Spoon

X > Z > Y

X != 5, therefore since X is largest, X > 5

(if X = 4, Z = 3 and Y = 2, there would be one empty box)

Therefore, Z < 4

(if X = 6 (lowest possible value), and Z = 4, There would be no Y, and that's not possible)

Possible solutions so far

X = 6
Z = 3
Y = 1

X = 7
Z = 2
Y = 1

At least one of each utensil so Y cannot be 0

Z!= 3

so far must be

X = 7
Z = 2
Y = 1

Y !=Z/2

So cancelling above solutions.

Therefore, as n_fortynine said, there is no solution.
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LVL 9

Expert Comment

ID: 8181199
I agree that there does not appear to be a correct solution.

The last statement:

>: A fork is not in precisely half the
>number of boxes a spoon is in.

This can be interpreted two ways:

1) F <> 0.5 * S
2) 10 - F <> 0.5 * S

Either way, it still appears that there is no solution.
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LVL 13

Expert Comment

ID: 8181407
I agree. There is no solution.
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LVL 24

Expert Comment

ID: 8181552
k>s
s>f
k<>5
s<>3
f<>s/2
Oops, skipped something... "There is at least one of each utensil"
so k>s>f>0 and k+s+f=10
hmm, any comment to reply to the above, skelmoogies?
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LVL 24

Accepted Solution

SunBow earned 200 total points
ID: 8181741
If I did this right, here are the only four solutions to:
so k>s>f>0 and k+s+f=10

fork                              spoon                             knife
1)       1                                    2                                    7
2)       1                                    3                                    6
3)       1                                    4                                    5
4)       2                                    3                                    5

k<>5 eliminates #3 & #4
s<>3 eliminates #2 & #4
f<>s/2 eliminates #1

So, the crafter has eliminated all possible integer solutions. So far, for the mathematics, the opinions remain unanimous.

Now, what about the Riddle? (and where's the help needed?) Maybe the first comment, that one of the statements is false.
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LVL 13

Expert Comment

ID: 8181809
If any of the statements is false there become more than one soluition unless the false statement is f<>s/2 so the answer must be
f=1 s= 2 k=7
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LVL 24

Expert Comment

ID: 8181828
> : A fork is not in precisely half the number of boxes a spoon is in.
> and each box contains one object

Best I can do now with semantics is that:

"A fork is never in the same box a spoon is in, in any proportion"

This is a stretch IMO, and perhaps unfair, but it removes constraint of f<>s/2 so my #1 above would pass remaining tests. So here's alternative solution:

1 fork, 2 spoons, 7 knives                               :-(
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LVL 8

Expert Comment

ID: 8181865
I can see 2 options :

1.  "There is a row of ten boxes and each box contains one object, which is a knife, a fork or a spoon."
It does not say "only one object" so does this mean that I can have a knife and a spoon, or a knife and a fork.  If it said "either a knife or a fork or a spoon" then it would eliminate the possiblity of more than one in a box, but since it doesn't then maybe......

2.  I am talking b****cks and there is no solution.

skelmoogies - can you give us a clue
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LVL 24

Expert Comment

ID: 8181901
Aw, andycrofts beat me to that one. I disagree only a little on justification because of:

> Here are five true statements

which still adds complexity. But nice argument, IMO.

While there could be teaspoon vs soup spoon issue, I don't see how to squeeze an argument in.

Take word replacement, change "five" to "four" as the answer to the problem in original question. Now you get:

> Here are four true statements
> : A knife is not in precisely four boxes.

now the number of solutions is more open. So,,, I'll revert to my original mistake, and claim that this is the false statement:

> There is at least one of each utensil

This enables:
0 fork, 0 spoon, 10 knife
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LVL 24

Expert Comment

ID: 8181968
debbie,
How far off are we here, how're we doin'?
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LVL 4

Expert Comment

ID: 8181997
>> MusicMan: It does not say "only one object" so does this mean ...
No, because then it would have said "at least one object." The English semantic in the sentence is clear (oh maybe missing "EITHER a spoon...")!
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LVL 8

Expert Comment

ID: 8182065
Bollocks, I think SunBow has got it.
"A fork is not in precisely half the number of boxes a spoon is in."
Of course it's not, it's not in any of the boxes that a spoon is in, because the spoon is already in there and each box contains one item.

Nice one Sunbow!!
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LVL 1

Expert Comment

ID: 8182435
i would say that there are
6 knives in 6 boxes
4 spoons in 4 boxes
and up either 1 or 3 forks which are not represented in a box but do exist outside.

this way:
There is a row of ten boxes and each box contains one object, which is a knife, a fork or a spoon.  = true

There is at least one of each utensil. = true
and the five conditions are true...maybe?we'll see

:)
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Author Comment

ID: 8183086
thank you all you guys, the answer was indeed 5 knives 4 spoons and 1 fork, i hardly slept last night and the bit that confused me was the last sentence about there not being precisley half of the spoons bit,and i was trying to work out with half the number of spoons for the forks, and i was wrong because if you think about it, it is telling you that there is NOT half the spoon amount........ so it had to be an uneven number to the spoons

AND SUNBLOW GOT IT RIGHT.....

OH and one other thing, i do not know how this points system works, i know it says i gave 50 points, but in my last posting i think something went wrong and someone thought they got robbed... so i apologise if this one goes wrong, i am only following what the instructions tell me to do....so please forgive me if it is wrong..
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Author Comment

ID: 8183092
thanks for your help.... how long did it take you to work it out, it took me all night and i finally got it this morning at about 8 while at work
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LVL 24

Expert Comment

ID: 8183179
Thanx, I didn't expect you back so soon. I gotta rush out, but before passing your work to another, do revisit your constraint:

> : A knife is not in precisely five boxes.

Or, I'm confused, but no more than usual.

> last posting i think something went wrong and someone thought they got robbed...

Not to worry. My memory has it that it was a thread on "robbing" and a comment was more wisecrack - alternative form of joke.

>  forks which are not represented in a box but do exist outside.

hmm, interesting.
In interim, I wondered if "utensil" might be trick, something other than we intuit. I may just check out dictionary later.

btw, no "L" in SunBow, but I'm not insulted.               :-)
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LVL 9

Expert Comment

ID: 8183352
I am glad I started the idea about semantics -- I remember that most of these that are "unsolvable" center on semantics. Still, I don't see how SunBow gave that answer except to expand on my assertion of "statements" being taken two ways. Now, I can see how a previous poster felt he was "robbed". LOL
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LVL 13

Expert Comment

ID: 8184596
Ahh! It is like " I have two coins that total 70p and one of them is not a 50p"

"A knife is not in precisely five boxes."
so a knife is in every one of the other five boxes!
LOL
I love this one!
Top puzzle :-)
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LVL 13

Expert Comment

ID: 8184602
BTW the one that is the 20p is the one that is not a 50p
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Expert Comment

ID: 8184609
I don't see anyone who got 5 4 1 ??
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LVL 24

Expert Comment

ID: 8184894
Hey , I got it, as #3 of my first four reductions. (but I then refuted it with the constraint)

andycrofts> BTW the one that is the 20p is the one that is not a 50p

I think you got it, I'll defer the dictionary then. I've but one question on your justification, for this should get same treatment:

> : A spoon is not in precisely three boxes.

so, seven spoons?

I gotta go before my head spins and I forget the weekend approacheth
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LVL 13

Expert Comment

ID: 8194316
> : A spoon is not in precisely three boxes.

so, seven spoons?
Yes that occurred to me after I'd left the computer.

This can't be the answer but it is inconsistent interpretations of the statements.
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