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.

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).

(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.

0

Protecting against advanced threats requires an IT dream team – a well-oiled machine of people and solutions working together to defend your organization. Download our resource kit today to learn more about the tools you need to build you IT Dream Team!

k>s
s>f
k<>5
s<>3
f<>s/2
How about k=10?
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?

> : 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. "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.

>> 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...")!

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.

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

:)

0

skelmoogiesAuthor Commented:

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..

0

skelmoogiesAuthor Commented:

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

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

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.

0

Featured Post

Evaluating a UTM appliance and vendor can prove to be an overwhelming exercise. How can you make sure that you're getting the security that your organization needs without breaking the bank? Check out our UTM Buyer's Guide for more information on what you should be looking for!