# Thread: The grass is always greener

1. The other day Jezza Bear was out for his Sunday morning run and was just taking a little
rest by leaning on Farmer Cubbly's gate. As he admired the herd of 6 cows in the field
Farmer Cubbly appeared.

"Hello Jezza Bear, I put these 6 cows in this field and it has taken them 3 days to eat all the grass"

"That is interesting Mr Cubbly"

"What I plan to do JB is put the cows in the other field, let the grass grow back to the original height
and then let only 3 cows back in"

"Sounds like a plan Mr Cubbly"

"My question to you JB is how long will it take the 3 cows to eat all the grass?"

NB Jezza Bear has already been assured that the cows all eat at a constant rate

2. <span title="Spoiler: Highlight to reveal" style='color:#000000;background:#000000;padding:0p x 0.2em;'>[color=#666;margin-right: 0.2em]SPOILER:[/color]Doesn't it depend on how quickly the grass grows? If the grass grows back in three days (I think) they may never finish.</span>

3. [quote name='Leif' post='785174' date='18-Jul-2009 08:32']<span title="Spoiler: Highlight to reveal" style='color:#000000;background:#000000;padding:0p x 0.2em;'>[color=#666;margin-right: 0.2em]SPOILER:[/color]Doesn't it depend on how quickly the grass grows? If the grass grows back in three days (I think) they may never finish.</span>[/quote]

Good point....to clarify the puzzle.

Farmer Cubbly will put the 3 cows back in the field when the grass is the same height as when the experiment was done with 6 cows.

4. Any takers?

5. [quote name='Jezza' post='785384' date='20-Jul-2009 12:13']Any takers? [/quote]
Well, I still think <span title="Spoiler: Highlight to reveal" style='color:#000000;background:#000000;padding:0p x 0.2em;'>[color=#666;margin-right: 0.2em]SPOILER:[/color]the speed of grass growth comes into it. In theory, half as many cows will take twice as long, but I can't believe it is as straightforward as that! Were the three cows that were let back in allowed to eat during the time the grass was growing back? Are there any sheep in the field with them? Was it raining? Does your chewing gum lose it's flavour if you leave it on a gate-post overnight?</span>

6. [quote name='Jezza' post='785384' date='20-Jul-2009 05:13']Any takers? [/quote]

There are too many unknowns to come to a firm conclusion. One thing that is not mentioned is whether the six cows all eat at the same rate. You clarified that they eat at a constant rate, but if three cows do all the work and the other three are slackers, then the answer could be three days if the three workers are put back to graze or never if the three slackers are put back. Assuming that they all eat at the Same constant rate then there are still problems as we don't know the growth rate, as Leif mentioned.
One thing that may come into play is the phrase "eat all the grass". This seems to imply that the growth rate wasn't too rapid, other wise it would be hard to get to a time when "all the grass" was eaten. If the growth rate is non-zero, all the grass could never truly be eaten. So some assumption has to be made about what "all the grass" means. If the growth rate was considerably lower than the eating rate, then three cows would take possibly only a little more than six days.
If the growth rate were higher, then it is possible that three cows could never eat all the grass.
This reminds me of the water flowing into and out of a tub differential equations from college days.

7. Precipitation? Alfalfa? Crop rotation versus cow rotation? Crop circles? Can this grass be smoked? Is this farmer starving three cows to satisfy your craving for puzzles? Are you feeling your oats? Surely it's barely barley. Save the hops and have a beer. How does that nursery rhyme go about the rats and the malt and all that stuff. You haven't told us the breed of cow, nor even if they are all the same breed (or crossbreed). Puzzle unsolvable. Q.E.D.

8. I think we can scrap this puzzle, I have just realised I left a great chunk of the logic out. However I do think you are all looking at the one I presented just a little too deeply....just saying.

I'll repost the "proper" puzzle at a later date

9. Originally Posted by jezza
I'll repost the "proper" puzzle at a later date
Well, if Farmer Jezza put 1 puzzle up and it took 3 loungers 4 days to reduce Farmer Jezza to despair, how many lounge updates will pass before Jezza posts back in this thread?

10. Not long Chris.....in fact 56 minutes

11. If need be I will post the full (updated) puzzle but I didn't feel to inclined to continue this one as.....

12. This is Test D.

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