99gecko,

I am stuck. I believe I know what I need to do to figure it out but I just can't get there. Good one BTW!

Q

I keep picturing a horse eating the grass in front of him and as soon as he wants to leave that area, more grass keeps coming. Like he can never clear the field.

asif9t9,

I know you've got the right idea; you are seeing the problem as an issue of rates and how the reduction of grass approaches an asymptote; a barrier that prevents all of the grass from ever being gone.

In a way you are right, but if it helps you visualize it easier consider the problem with these added boundaries:

All of the animals are nocturnal. i.e. they only eat grass at night.
The grass only grows during the day, i.e. as opposed to the original presentation where I stated the grass grows continuously.

What this means is when the animals finish eating grass during their *nightshift*, the grass growing *dayshift* takes over. So if the animals succeed and finally finish eating all of the grass at the end of their shift (dawn), there is no grass remaining to continue growing when the sun comes up. These additional boundaries remove the issue of the asymptote.

But really the above is over complicating this puzzle. It might help some to just visualize it the way it was originally presented. In fact, if you are using a mathematical approach, use the original presentation, as the day/night stuff will really complicate things if you are trying to build formulae to account for parts of the day. Okay, ....geeez,.... I think I just confused myself. :o

Anyway, here's a hint for the weekend:
asif9t9, you're actually correct in a way, but you've got the wrong animal. The horse can eat the grass by itself. Remember that:
3. The goose and the sheep eat the grass in 90 days.
4. The horse eats the same amount of grass as the goose and the sheep together.
However, one of the animals will never finish the grass by itself.

I am stuck.
groan, ... I doubt that.

GLtA, and see you Monday :o

Another thing that has me a bit messed up. The horse eats the same as the goose and the sheep. Which means the horse alone would take 90 days. Which should mean two horses would take 45 days. But somehow one horse and one sheep are able to polish it off in 45 days. hmmm.....

This is the way I see it but after a few pages of calculations I gave up.....I might have screwed up an earlier equation which threw off later numbers.


every animal eats the grass at a certain rate so % or ratio of field / day. The key IMO is the ratio that the grass grows back / day.

asif9t9 2 horses would be much faster than 45days because less of the grass grows overall because 2 horses eat more per day

Q, you're on the right track.
every animal eats the grass at a certain rate so % or ratio of field / day. The key IMO is the ratio that the grass grows back / day.

Exactly! I've highlighted the word that shows you are thinking on the right track.

asif9t9, I know it may seem like twisted logic, but you have not considered that the grass is growing continuously. Your opposition is not quite right. It would be valid in a static environment; i.e. if the amount of grass was finite, which it is not since it can replenish itself. You must think in ratios as Q is doing.

Here's a free hint to get you going again: Which should mean two horses would take 45 days. But somehow one horse and one sheep are able to polish it off in 45 days. One horse, one sheep, and one goose, would polish it off in the same amount of time as two horses, which as Q has pointed out is less than 45 days.

I know it not so much of hint as it is a rewording of existing facts, so I will give a better hint tomorrow if this is still around.

I did screw up an early calculations which screwed up everything as I found out when I started over today.

The answer is 36 days.

I will post my math which is probably the harder way but the way I saw the problem later in day or when I get a chance tonight.

Goodluck!

Q

Well in a weird way, I stopped thinking about it and just went with math and determined that all three animals would work together at 2.5x the speed of just the horse. So if the horse is taking 90 days, then I get the same answer as Q.

I can't explain it, but it makes sense to me mathematically.

Eq 1: G + S = H = 90/90

Eq 2: H + G = 90/60 or G = 90/60 - H

Eq 3: H + S = 90/45 or S = 90/45 - H

H + G + S = 90/x

Use all three known equations (the bolded parts above), solve for x

90/90 + (90/60 - H) + (90/45 - H) = 90/x

1 + (1.5 - 90/90) + (2 - 90/90) = 90/x

1 + 1.5 - 1 + 2 - 1 = 90/x

2.5 = 90/x

x = 36

Here is math behind my answer if any one is interested.


h = horse
s = sheep
g = goose
gr = grass
x = days

h = g+s so I substituted that in for the equation. First equation is (g+s)+s in 45 days
Another thing to keep in mind is that it is 1 field so the above equation is 45(g+s)+45s-45gr = 1 which is 45 days of the goose, sheep and grass growing back to make 1 field with no grass.
So we get 90s+45g-45gr = 1

We also have 90g+90s-90gr = 1

Combine them to eliminate the common value of sheep
90s+45g-45gr = 90g+90s-90gr
45g = 45gr
g = gr

Since gr is equal to g
90s+45g-45gr=1
s = 1/90

plug in s and sub gr for g
120g+60(1/90)-60g = 1
60g = 1/3
g = 1/180 = gr

plug in s and g and gr to get h
45h+45(1/90)-45(1/180) = 1
45h+1/2-1/4 = 1
45h = 3/4
h = 3/180

Now plug in everything to get x (days) and since the goose cancels grass we eliminate those variables.
hx+sx+gx-grx = 1
3/180x + 1/90x = 1
5/180x = 1
x = 36

Correct, although I didn't follow asif9t9's solution completely, and Q did it a little differently than I. For those not willing to follow the equations (because I know that isn't everyone's cup of tea), here is the answer in plain English.

Therefore the H ate 1/2 the starting grass plus whatever new grass grew in 45 days.

Now, the H + S finish in 45 days, half the time as the H alone. But as stated, the H has eaten half of his 90 day total, which is 1/2 the starting grass + the growth of grass in 45 days.
What's left for the S to have eaten is the other half of the initial grass. So the S can eat the initial grass by itself in 90 days. The S needs the G's help to eat starting grass + 90 day's growth in 90 days, so it follows that the G eats grass exactly as fast as it grows.

The H + G can eat everything in 60 days. Which means (since the G cancels out any new growth) that the H can eat the initial grass in 60 days. The S took 90 days to eat the initial grass, so the H can eat 1.5 times as fast as the goat. And, since S + G = H, the G eats 0.5 times as fast as the S.

So (making 180 the common denominator so there are no decimals):
The H eats 1/60th (or 3/180) of the starting grass per day.
The S eats 1/90th (or 2/180) of the starting grass per day.
The G eats 1/180th of the starting grass per day.
The grass grows at 1/180th of the starting grass per day.

So all three eating together plus the grass growing means a reduction of 5/180 of the starting grass per day, or 1/36th per day.
Or,….they finish in 36 day

Well done to both of you. :D :D :D Much faster than I expected.

so,.....who's next?

Here's one with less math involved :):
How quickly can you find out what is unusual about this paragraph? It looks so ordinary that you would think that nothing was wrong with it at all, and in fact, nothing is. But it is unusual. Why? If you study it and think about it you may find out, but I am not going to assist you in any way. You must do it without coaching. No doubt if you work at it for long, it will dawn on you. I don't know. Now, go to work and try your luck.

The paragraph contains no words with the letter E

There is no letter "e"?

Sorry for the delay. Yes, that is correct for both of you.
It is the letter that is important, not the case. There are also no letter "x" or "z", however they aren't common in English language. Incidentally the letter "e", is the most common in the English language - code breakers learn this on Day One of Cryptology 101 ;)

I'll have a new puzzle for you in a moment.

You have 9 ping pong balls in a bag, and a balance scale.

http://www.ornl.gov/sci/scale/images/scale_wallpaper.gif

One of the ping pong balls is filled either with some helium so it is lighter than the other eight balls, or with argon so it is heavier than the other eight balls. The other eight balls all weigh the same.

What is the minimum number of weightings needed to definitively determine which ping pong ball has the helium? That is, how many times must you do weightings to absolutely identify the ball, regardless of it's position in the bag?

good luck

BTW, if anyone else has puzzles to post - fire away.

On another forum that I visit, the protocol is that once the correct answer to a puzzle has been verified by the member who posted the question, the member who answered correctly first gets to post a question. If the consensus agrees, we could follow that method here perhaps???

I would say 3 weighings,

4 / 4 then 2 / 2 then 1/ 1

sorry that was too easy thought there were 8 balls & not 9

And remember,....
You don't know whether the ball is heavier or lighter than the others. All you know is that one of them is different.

I almost posted with confidence 2. But then I saw your note about not knowing if the ball is heavier or lighter... Let me think some more...

Here's a new one I don't recall seeing in here yet:
What's the next line in the following sequence:
3
1 3
1 1 1 3
3 1 1 3
2 3 2 1
2 2 1 3 1 1