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# Tag Archives: tree

## Computing optimal play for the greedy coins game, part 4

Last time I explained a method for computing best play for instances of the greedy coins game, which is feasible even for large games. This general approach is known as dynamic programming and is applicable whenever we have some recursively … Continue reading

Posted in computation, games, recursion
Tagged coins, dynamic, game, optimal, play, programming, proof, recurrence, strategy, tree, two-player, zero-sum

## Computing optimal play for the greedy coins game, part 3

In a previous post we saw how we can organize play sequences in the greedy coins game into a tree. Then in the last post, we saw how to work our way from the bottom of the tree upward and … Continue reading

Posted in computation, games, recursion
Tagged coins, game, optimal, play, proof, recurrence, strategy, tree, two-player, zero-sum
2 Comments

## Computing optimal play for the greedy coins game, part 2

I want to explain in more detail how we can think about computing the best possible score for Alice in the greedy coins game, assuming best play on the part of both players. I glossed over this too quickly in … Continue reading

Posted in computation, games, recursion
Tagged coins, game, optimal, play, proof, recurrence, strategy, tree, two-player, zero-sum
1 Comment

## Apollonian gaskets

In my last post I showed off this tantalizing picture: This pattern of infinitely nested circles is called an Apollonian gasket. Over the next post or two I’ll explain some cool math behind actually constructing them. Mostly I will state … Continue reading

Posted in geometry, pattern, pictures, recursion
Tagged Apollonian, gasket, recursion, tree
4 Comments

## The hyperbinary sequence and the Calkin-Wilf tree

And now, the amazing conclusion to this series of posts on Neil Calkin and Herbert Wilf’s paper, Recounting the Rationals, and the answers to all the questions about the hyperbinary sequence. Hold on to your hats! The Calkin-Wilf Tree First, … Continue reading

Posted in arithmetic, computation, induction, iteration, number theory, pattern, proof, recursion, sequences, solutions
Tagged algorithm, binary, Calkin-Wilf, Euclidean, Haskell, hyperbinary, tree
6 Comments