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Tag Archives: conjecture
The curious powers of 1 + sqrt 2: recurrences
In my previous post, we found an answer to the question: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? However, the solution depended on having the clever idea to add . … Continue reading
Posted in number theory, puzzles
Tagged conjecture, digits, powers, puzzle, ratio, silver
8 Comments
The curious powers of 1 + sqrt 2: a clever solution
Recall that we are trying to answer the question: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? In my previous post, we computed for some small and conjectured that the answer … Continue reading
Posted in number theory, puzzles
Tagged conjecture, digits, powers, puzzle, ratio, silver
2 Comments
The curious powers of 1 + sqrt 2: conjecture
In my previous post I related the following puzzle from Colin Wright: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? Let’s play around with this a bit and see if we … Continue reading
Posted in number theory, puzzles
Tagged conjecture, digits, powers, puzzle, ratio, silver
3 Comments
Another greedy coins game update
Another update on the analysis of the greedy coins game (previous posts here, here, and here). I will make another post very soon explaining how to compute optimal play. In my previous post I reported that Thibault Vroonhove had conjectured … Continue reading
Posted in games, proof
Tagged coins, conjecture, game, proof, strategy, twoplayer, zerosum
Comments Off on Another greedy coins game update
Greedy coins game update
I plan to write a longer post soon, but for the moment I just wanted to provide a quick update about the greedy coins game (previous posts here and here). It turns out that the game is a lot more … Continue reading
Posted in games, proof
Tagged coins, conjecture, game, proof, strategy, twoplayer, zerosum
18 Comments