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# Category Archives: solutions

## Post without words #5, explained

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 curve, Hilbert, Prouhet-Thue-Morse, sequence, space-filling, Thue-Morse
3 Comments

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

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

## The birthday candle problem: solution

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 birthday, candles, expectation, problem
5 Comments

## The Steinhaus-Johnson-Trotter algorithm

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 algorithm, change, permutations, ringing, SJT, swap
9 Comments

## Fun with repunit divisors: more solutions

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 repunit

## Cassini’s identity

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