The problem description. The solutions 3 ways to solve it.
I took the challenge and thinking that the students participating the mathematical kangaroo contest have about 2 1/2 minutes per problem, I thought 30 min would be fair looking for an elegant solution. Don't looking at the choices at first hand.
And I failed
When you start, It's just you and the problem and your ideas. And your ideas are influenced by your knowledge, skills and tools. I am an Algebraist by education, a kind of abstractonaut driving things up to the "abstract nonsense" (Recall, the free algebraic structures in the freedom of a financial language).
Not bad for formal language structures, symbolic computation, functor programming, pattern matching programming, ….
However, my try: find a closed form solution. I did suppress that there are states and transitions and that a rule base that describes the constraints is also an analytic solution.
Not surprisingly, I did not find it. Time out
With Andreas' elegant solution you only need to know what even and odd numbers are and a simple inference engine for the rule base deducing new knowledge.
Andreas is sure that children of the age of 9 years could solve the problem with a few hints.
Children are "scientists" as well - outside "official"settings?
Deep, Beautiful and Elegant Explanations
After knowing the solution, I, by chance, looked for the current best sellers in science and maths and found: This Explains Everything - 150 Deep, Beautiful and Elegant Theories of How the Word Works, in short Essays.
There are all sorts of answers to: what is your favorite deep, beautiful or elegant explanation? One just wrote "keep it simple" and then crossed it out. One explained why "elegant=complex".
Edit: I need to confess a litte dishonesty: I started with a strategy (thinking wolves ..):
(1) 6 lions devour 6 goats: (17, 55, 6) -> (11, 61, 0)
(2) 6 wolves devour 6 goats: (11, 61,0) ->(5, 55, 6)
(3) 6 lions devour …. uuups
(and said to myself: stop trying, solve! - and the headache began)
BTW, this strategy had worked with 18 goats (not 17) leading to (0, 61, 0). What a nice puzzle!
Picture from sehfelder (the lonesome "solver" and the possible paths ;))
Picture from sehfelder (the lonesome "solver" and the possible paths ;))
