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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

## 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 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

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