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.
represent the amount of G
rass in the field at the start.
represent the amount of grass that g
rows each day.
represent the amount of grass one goat eats in one d
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
From which we can work out that
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.]