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Original source (unriskinsight.blogspot.com)
Clipped on: 2014-06-05
Goats, Wolves and Lions
This is a puzzle from the Austrian 2014 mathematics kangaroo contest, taken from the students' level (16years and older), which was brought to me by a friend, who is high school teacher. I think, this is really a challenging and nice one. Remember that this puzzle is one of 30 puzzles (albeit the most difficult one), and the contestants have 75 minutes of time for all of them.
I will probably publish my solution on Wednesday. I am waiting for your answers (see below what I mean with an "answer") until Wednesday noon to Andreas Binder.
The puzzle
There are three species of animals in a magic forest: lions, wolves and goats. Wolves can devour goats, and lions can devour wolves and goats. ("The stronger animal eats the weaker one".) As this is a magic forest, a wolve, after having devoured a goat, is transmuted into a lion; a lion, after having devoured a goat, is transmuted into a wolve; and a lion having devoured a wolve becomes a goat.
At the very beginning, ther are 17 goats, 55 wolves and 6 lions in the forest. After every meal, there is one animal fewer than before; therefore after some time, there is no devouring possible any more.
What is the maximum number of animals who can live in the forest then?
A super-correct answer in my understanding
A correct answer contains
(a) the number of animals left,
(b) a devouring strategy leading to this number
(c) the proof that this is the maximal possible number of animals left.
Two versions of the puzzle: The even more difficult one.
The even more difficult one does not give you possible answers for (a). This is thought for the geniuses among you.
The kangaroo version is a multiple choice test, giving you 5 possible answers. I will write down these possible answers below the pictures. Therefore, geniuses, stop reading now.
I will probably publish my solution on Wednesday. I am waiting for your answers (see below what I mean with an "answer") until Wednesday noon to Andreas Binder.
The puzzle
There are three species of animals in a magic forest: lions, wolves and goats. Wolves can devour goats, and lions can devour wolves and goats. ("The stronger animal eats the weaker one".) As this is a magic forest, a wolve, after having devoured a goat, is transmuted into a lion; a lion, after having devoured a goat, is transmuted into a wolve; and a lion having devoured a wolve becomes a goat.
At the very beginning, ther are 17 goats, 55 wolves and 6 lions in the forest. After every meal, there is one animal fewer than before; therefore after some time, there is no devouring possible any more.
What is the maximum number of animals who can live in the forest then?
A super-correct answer in my understanding
A correct answer contains
(a) the number of animals left,
(b) a devouring strategy leading to this number
(c) the proof that this is the maximal possible number of animals left.
Two versions of the puzzle: The even more difficult one.
The even more difficult one does not give you possible answers for (a). This is thought for the geniuses among you.
The kangaroo version is a multiple choice test, giving you 5 possible answers. I will write down these possible answers below the pictures. Therefore, geniuses, stop reading now.
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