[pdurrant]

Originally Posted by orlok

Is the answer forever, then, as the grass will keep regrowing, and with only 3 sheep they won't eat it fast enough to run out before more has grown?

Yes! Exactly so.

Let G represent the amount of Grass in the field at the start.
Let g represent the amount of grass that grows each day.
Let d represent the amount of grass one goat eats in one day.

The we know that after 7 days, 11 goats will have eaten all the grass.

The amount of grass 7 goats eat in 11 days = 7 * 11 * d
The amount of grass (if uneaten) after 7 days = G + 7 * g

77*d = G+7g

Similarly,

80*d = G+8g

From which we can work out that

3*d = g

That is, the amount of grass that grows each day (g) is exactly equaly to the amount of grass eaten by 3 goats (3*d).

So with three goats in the field, the grass renews itself every day, and the goats can graze indefinitely.

Over to you!


[I should credit Richard Wiseman's blog for the puzzle.]