Quote:
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+7
g
Similarly,
80*
d =
G+8
g
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.]