Tag Archives: puzzle

The wizard’s rational puzzle (solutions, part 2)

Posted on November 9, 2018 by Brent

At long last, here is the solution I had in mind for the Wizard’s rational puzzle. Recall that the goal is to figure out the numerator and denominator of a secret rational number, if all we are allowed to do … Continue reading →

Posted in arithmetic, challenges, logic, programming, puzzles, solutions | Tagged arithmetic, binary, denominator, Euclidean, gcd, logarithm, numerator, puzzle, rational, search, wizard | Comments Off

The wizard’s rational puzzle (solutions, part 1)

Posted on October 24, 2018 by Brent

About two and a half months ago I posted a challenge involving a sadistic math wizard, metal cubes containing rational numbers, and a room full of strange machines. I’ve been remiss in following up with some solutions. (Go read the … Continue reading →

Posted in arithmetic, challenges, logic, programming, puzzles, solutions | Tagged arithmetic, denominator, Euclidean, gcd, logarithm, numerator, puzzle, rational, wizard | 3 Comments

The wizard’s rational puzzle (mind your p’s and q’s!)

Posted on August 7, 2018 by Brent

You have been abducted by a sadistic math wizard (don’t you hate it when that happens?). He ushers you into a plain but cozy-looking room, with a hardwood floor, a few exotic-looking rugs, and wood paneling on the walls. He … Continue reading →

Posted in arithmetic, challenges, logic, programming, puzzles | Tagged arithmetic, denominator, numerator, puzzle, rational, wizard | 15 Comments

The curious powers of 1 + sqrt 2: recurrences

Posted on July 6, 2017 by Brent

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

Posted on June 21, 2017 by Brent

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

Posted on June 17, 2017 by Brent

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

The curious powers of 1 + sqrt 2

Posted on June 6, 2017 by Brent

Recently on mathstodon.xyz, Colin Wright posted the following puzzle: What’s the 99th digit to the right of the decimal point in the decimal expansion of ? Of course, it’s simple enough to use a computer to find the answer; any … Continue reading →

Posted in challenges, number theory, puzzles | Tagged powers, puzzle, ratio, silver | 15 Comments

The route puzzle

Posted on June 17, 2016 by Brent

While poking around some old files I came across this puzzle: (Click for a larger version.) I didn’t make it, and I have no idea where I got it from (do you know?). But in any case, wherever it comes … Continue reading →

Posted in arithmetic, challenges, number theory, proof, puzzles | Tagged cube, perfect, prime, puzzle, route, square, triangular | 7 Comments

The wonderful world of Mike Reilly

Posted on June 14, 2011 by Brent

The other day I received an email from Mike Reilly, who introduced himself as a professional game and puzzle inventor, and suggested that I might be interested in taking a look at a few of his web sites. I wasn’t … Continue reading →

Posted in games, links, people, puzzles | Tagged cube, hour, Kickstarter, maze, puzzle, Reilly | 2 Comments

My blog is back (hooray!) and a quick puzzle

Posted on February 22, 2011 by Brent

My blog is finally back up after a long hiatus due to hosting problems (not the first time). I’m seriously contemplating moving somewhere more reliable, but it’s hard to come up with a solution that would not (a) invalidate any … Continue reading →

Posted in logic, meta, puzzles | Tagged logic, puzzle, quiz, surprise | 8 Comments