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Category Archives: puzzles
The wizard’s rational puzzle (solutions, part 2)
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 on The wizard’s rational puzzle (solutions, part 2)
The wizard’s rational puzzle (solutions, part 1)
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!)
You have been abducted by a sadistic math wizard (don’t you hate it when that happens?). He ushers you into a plain but cozylooking room, with a hardwood floor, a few exoticlooking 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
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
The curious powers of 1 + sqrt 2
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
The route puzzle
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
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
Area paradox unmasked
In my last post I presented a paradox, where a set of four pieces forming an 8×8 square could apparently be rearranged to form a 5×13 rectangle, summoning an extra unit of area out of thin air. Quite a few … Continue reading