Find the simplest way to solve this....

[Vain]

5000 WGDs if you want them

...without a formula

There are a number of horses and chickens standing in a field.

If I add all the legs together, I count 40 legs

How many horses and how many chickens are there?

[I'm Murrin]

Unless there's some trick to the question there are multiple possible answers?

10 horses, or
9 horses 2 chickens, or
8 horses 4 chickens, or
7 horses 6 chickens, or
6 horses 8 chickens, or
5 horses 10 chickens
etc
etc
And that's only assuming they all have a full set of legs.

[Vain]

There's only one right answer...and yes they all have all their legs

[TheFallen]

The number of chickens = 20 - twice the number of horses.

The number of horses = 10 - half the number of chickens.

Wait - do those count as formulae?

There's seriously only one answer?

[Vain]

Forty legs in total means that 10 horses already have 40 legs. There's a mix of horses and chickens

And yes. There is only one right answer and it can be logically deduced

[TheFallen]

If the total number of legs had been 42, then I would have said the answer was seven.

Vain saw "a number of horses and chickens"... that number would have been seven... seven horses and seven chickens... if ONLY the total had been 42 legs.

Sheesh... no partial amputee horses allowed, I notice. *sigh*

Vain, this must have something to do with a strict interpretation of the word "number". Or "count". Or "standing", for that matter. Or possibly some of the chickens are standing on the backs of the horses... but I don't see how that helps anything. Nor does it help if you add your own legs into the equation. That'd only work if the total was 38. 6 horses = 24 legs, 6 chickens = 12 legs, Vain = 2 legs. Total 38.

Or maybe it's not a field with grass - maybe it's an electromagnetic field or something. But I dunno how that helps either.

[I'm Murrin]

There are still lots of possible answers. Either the riddle's poorly asked or you're mistaken that there's only one answer.

Edit: A little googling shows that the usual form of this puzzle is to name the number of legs and the number of heads, so that there is only one correct answer.

[Fist and Faith]

Did you include your own legs? Does it matter if some of the chickens are riding horses?

[TheFallen]

GMTA, FnF

[Hashi Lebwohl]

I would be to differ with the statement that there is only one correct answer but I do not beg. I do, however, concur with I'm Murrin--there are multiple correct answers whether or not you are counting your own legs. If you are not counting your own, then the solution is in the set [in the form (chickens, horses)] of {(18,1), (16,2), (14,3), (12,4), (10,5), (8,6), (6,7), (4,8), (2,9)}. If you are standing in the field then subtract one from the number of chickens.

There must be one other fact which would introduce a limiting factor that would distill the set of solutions down to only one result.

Most optimization problems have either a boundary solution or the solution in the very center of the results, which would leave us with (18,1), (10,5), or (2,9) and the maximum value of (number of chickens)x(number of horses) is found at (10,5).

[TheFallen]

Given that Vain's been very firm about there only being one solution, I'm assuming that there's no omitted fact. Instead, I suspect the hidden fact lies in the semantics of his statements...I just don't know where.

[Fist and Faith]

My bet is Murrin's right about the heads.

[wayfriend]

Maybe the number of heads is burried in the clue.

"white gold dollars"... if you subtract the letters that spell "heads", you get "wi gold ollr". This is a reference to Wisconson Gold Old Leafsprung Land Rovers. The blue-book value on a gold-colored old leafsprung landrover registered in Wisconson is $19K. ... if you take a way 5000 WGDs, that leaves $14K.

There are fourteen heads. 6 horses, 8 chickens.

Easy.

[Vraith]

6 horses [24 legs] 6 chickens [12 legs] me [2 legs] asking vain [2 legs] which chicken is the one who crossed the road=40 legs and a chicken crossing the road joke.

[Vain]

You guys are funny

But to be clear, the riddle is complete. No tricks. No hidden heads, or legs, or chickens sitting on horses, or animals with missing legs....or chickens crossing the road :D:D

And there still is only one right answer and it can be deduced through logic.....

[I'm Murrin]

Well you're going to have to tell us because I guarantee you no one will be able to tell you what you're asking for, because your riddle doesn't contain any information that allows any of the possible answers to be eliminated.

[Fist and Faith]

My son thought maybe no animals are in the field, just a bunch of severed legs.

[Hashi Lebwohl]

*shrug* Group by similarity--10 horses and 20 chickens, giving 40 horse legs and 40 chicken legs.

[Vain]

hrm...this will teach me not to translate my chinese friends' riddle

I omitted a factoid that has been pointed out....there's 15 heads (animals)

Using a formula you could say:

4x + 2y = 40 where x=horses and y=chickens

and

x + y = 15

y = 15 - x
therefore

4x +30 - 2x = 40

2x = 10

therefore x = 5 and y = 10

But there's a simpler way without ye olde xy formula...shall i save myself further embarrassment by just revealing it?

[TheFallen]

You can actually be saved any amount of embarrassment at this point in proceedings?