Category Archives: solutions

Probabilistic PIE

Posted on July 17, 2019 by Brent

Commenters Sylvain B., xpil, and Christian Luca all gave correct answers to the challenge from my previous post. If the probability that someone likes X is , then the probability they don’t like X is . Therefore the probability that … Continue reading →

Posted in pattern, probability, solutions | Tagged , | 7 Comments

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 , , , , , , , , , , | Comments Off on The wizard’s rational puzzle (solutions, part 2)

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 , , , , , , , , | 3 Comments

Post without words #5, explained

Posted on February 7, 2016 by Brent

If you stared for a while at the images in my previous post, you probably noticed some patterns, and maybe you even figured out some sort of rule or algorithm behind them. Commenter Yammatak expressed it as “You split it … Continue reading →

Posted in pattern, pictures, posts without words, sequences, solutions | Tagged , , , , , | 4 Comments

The chocolate bar game: losing positions proved

Posted on January 23, 2016 by Brent

In my last post I claimed that the losing positions for the chocolate bar game are precisely those of the form (or the reverse), that is, in binary, positions where one coordinate is the same as the other with any … Continue reading →

Posted in games, pattern, pictures, proof, solutions | Tagged , , , , , , , , | 4 Comments

A new way to read (and print) double-sided paper

Posted on January 8, 2016 by Brent

Continuing with the theme of reading stacks of paper (see my previous two posts, I have had a marvellous idea (at least I think so; I will let you judge for yourself). Let me take you through my thought process, … Continue reading →

Posted in pattern, solutions | Tagged , , , , , | 11 Comments

The birthday candle problem: solution

Posted on August 25, 2015 by Brent

Recall the birthday candle problem I wrote about in a previous post: A birthday cake has lit candles. At each step you pick a number uniformly at random and blow out candles. If any candles remain lit, the process repeats … Continue reading →

Posted in combinatorics, probability, solutions | Tagged , , , | 5 Comments

The Steinhaus-Johnson-Trotter algorithm

Posted on January 3, 2013 by Brent

In a previous post I posed the question: is there a way to list the permutations of in such a way that any two adjacent permutations are related by just a single swap of adjacent numbers? (Just for fun, let’s … Continue reading →

Posted in combinatorics, pattern, solutions | Tagged , , , , , | 9 Comments

Fun with repunit divisors: more solutions

Posted on November 17, 2011 by Brent

In Fun with repunit divisors I posed the following challenge: Prove that every prime other than 2 or 5 is a divisor of some repunit. In other words, if you make a list of the prime factorizations of repunits, every … Continue reading →

Posted in arithmetic, iteration, modular arithmetic, number theory, primes, programming, proof, solutions | Tagged | Comments Off on Fun with repunit divisors: more solutions

Cassini’s identity

Posted on May 15, 2011 by Brent

My previous post asked you to take any Fibonacci number, square it, and also multiply the two adjacent Fibonacci numbers, and see if a pattern emerged. Here’s a table I made for the first 6 Fibonacci numbers: (Hmm, the numbers … Continue reading →

Posted in algebra, fibonacci, induction, pattern, proof, solutions | Tagged , , | 8 Comments