Island of cats, birds, and snakes.?

Question

An island contains cats, birds and snakes. Each day each cat eats a bird for breakfast, each snake has a cat for lunch and each bird has a snake for supper. There are no births or deaths except at these meals.

At a certain time on the n-th day of the month, a bird becomes the only living creature left on the island. What time of day did this happen (i.e. at what meal)? Find an expression (or write a program) to evaluate the number of birds before breakfast on the first day of the month, in terms of n.

john · Accepted Answer

this happened at supper

as for n  days, suppose there are initially 
n+1 birds, n cats and n snakes

on first day one bird is consumed at breakfast
one cat is consumed at lunch and a snake is consumed at supper


so we are left with 
n birds
n-1 cats
n-1 snakes

continuing the same way
on the (n-1)th day at supper we are left with

2 birds
1 cat
1 snake

so on the nth day

the cat eats a bird at the breakfast

at lunch that last cat is eaten by snake

that snake is eaten by the only bird left at supper

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Island of cats, birds, and snakes.?

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