Question

LGBARIDDLE

You have 100 pet food that you're supposed to feed to 16 pets (made up of dogs, cats and mice). You must give 5 pet food to each mouse. Then 6 pet food to each cat, and lastly 8 pet food to each dog. How many dogs, cats and mice are there all in all?

Note: you can NOT use algebra. But you SHOULD use a logical method (not trial and error)

Answer 1

Give out pet food in bunches: feed 1 mouse, 1 cat, and 1 dog, then if you have food left over do it again. Repeat until all food is gone.

Answer 2

I'm not entirely sure if that would work, but...

Those are some hungry mice, by the way.

Answer 3

no algebra???

Answer 4

http://www.wolframalpha.com/input/?i=integer+solution+5x%2B6y%2B8z%3D100

Answer 5

@exitfreshly so how many cats, mouse and dogs?

Answer 6

@experimentX logical method

Answer 7

Can I use algebra to check my answer or is that cheating? XD

Answer 8

no algebra

Answer 9

it's impossible with algebra anyway

Answer 10

2 mice 11 cats 3 dogs

Answer 11

@experimentX i repeat...logical method

Answer 12

why isn't that correct?

Answer 13

Yeah, I have nothing. experimentX and his wolframalpha seem to have an answer, but I dunno how that computer got there.

Just out of interest, do you have an answer to the riddle, or is it impossible to solve?

Answer 14

logical method

Answer 15

yes it's possible with a logical method

Answer 16

you didn't use a logical method @experimentX

Answer 17

Oh, of course, but which one?

Answer 18

there are kinds of logical methods?

Answer 19

I should hope so, if there is more than one kind of math! Because math seems pretty logical to me.

Answer 20

logical => discrete mathematics => not algebra

Answer 21

can't you do this using Diophantine equations?

Answer 22

logical method....

Answer 23

that means no algebra..no equations

Answer 24

just disagreeing with "it's impossible with algebra anyway"

Answer 25

i doubt diophantine equation is applicable

Answer 26

how is it not applicable

Answer 27

because you can't use algebra

Answer 28

and how is trial and error not a logical method

Answer 29

So, now that we have gotten wonderfully technical and on tenterhooks, what's the answer to the riddle?

Answer 30

trial and error is never logical

Answer 31

i can find all possible combinations of 16, and test everyone
that is logical...

Answer 32

not really...

Answer 33

define:logical

Answer 34

discrete mathematics

Answer 35

if you want a formal definition http://en.wikipedia.org/wiki/Logic

Answer 36

how is finding all possible combinations of 16 and testing everyone not logical then?

Answer 37

you're a math lover. I'm sure you know..or at least can find out

Answer 38

Can we have a solution please?

Answer 39

please wait for some time... don't put the answer up yet

Answer 40

here are the ordered pairs: (mouse, cat dog)
(6,5,5),(4,8,4),(2,11,3),(0,14,2)

Answer 41

umm... also (8,2,6) :D

Answer 42

so that's it.... 5 solutions... please tell me if I'm wrong.

Answer 43

those aren't really solutions...those are answers...which again don't have logical methods @nipunmalhotra93

Answer 44

@lgbasallote they have logical methods

Answer 45

then by all means..share your "logical" method

Answer 46

remember..no algebr

Answer 47

sure,,,

Answer 48

make three columns.. mouse cat and dog. One box under every column represents one set of food packs required for them respectively. For example, if the box is under mouse, it represents a set of 5 food packs... likewise it represents a set of 6 and 8 food packs under cat and dog respectively.
We start by distributing packets one by one. We see that the arrangement in the diagram works.
For a solution to work, the total number of boxes should remain 16. Also, total number of packs should be 100.
So, we try to make different box arrangements in the above table.
One way is to take out 'a' boxes from M and put 'b' in C and 'c' D. So, 5a=6b+8d
and a=b+d which is not possible for +ve b and d.
Similarly taking out from D and putting in M and C is not possible.
So, the only way possible is to take out from M and D and put in C and vice versa.
With that, we get the above 5 solutions.
Now please do not say that I used 5a=6b+8d. It is just an innocent equation O:)