Alligators from the $\lambda$ park

Logic Level 3

Please read the rules of the Aligator Eggs game here

Addendum to the Color Rule: When the situation of conflict is removed, alligators revert to their original colors

These two families are called True and False respectively.

And here is a family called Not

When Not eats True , the result is False and when Not eats False , the result is True .

What should be the colors of the two eggs marked with ? be on the left and the right respectively?

This puzzle is borrowed from worrydream.com/AlligatorEggs/ , the best Lambda Calculus explanation I've ever seen

Green, Red Red, Red Red, Green Green, Green

1 solution

Tran Hieu
Apr 13, 2016

You really need to modify the color rules, maybe state that when eating lead to change color, after all done the color will change back. Otherwise this puzzle is unsolvable.

As I see it, the True family is any configuration of an alligator A on top of an alligator B on top of an egg C such that A and B have different colors and A and C have the same color; False family is any configuration where B and C have the same color instead of A and C. This is identical to the lambda term $(\lambda xy.x)$ and $(\lambda xy.y)$ ; renaming the variables (like, to $(\lambda zy.z)$ ) doesn't change it's meaning.

Ivan Koswara - 5 years, 2 months ago

The problem is that the rules of the game does not state $\alpha$ equivalence

Agnishom Chattopadhyay - 5 years, 2 months ago

Thanks! I've edited the problem. Does it look okay now?

Agnishom Chattopadhyay - 5 years, 2 months ago

Alligators from the λ \lambda λ park

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Alligators from the $\lambda$ park