A circle problem
A recent tweet by @iwontoffendyou posed the following problem: with reference to the figure below, what is the radius of the orange circle, which is tangent to the $y$-axis, the unit circle and the curve $y = \sqrt{x}$?
Puzzles
11 posts on puzzles. All posts · RSS feed
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The Goat Problem
A goat is tethered on the perimeter of a circular paddock of grass by a rope of length . What should be to allow the goat to graze on a maximum of half the area of the paddock? This is a famous problem in recreational …
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New York Times Spelling Bee solver
The New York Times publishes a daily puzzle, Spelling Bee, in which players must find as many words as possible using seven letters arranged in a hexagon. Each letter may be used any number of times but the solution words must be at least four …
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Making a word search puzzle in Python
The program given below takes a list of words and attempts to fit them into a grid with given dimensions to make a word search puzzle. For example, using the file planets.txt: produces the (cramped) grid puzzle: Various mask effects are implemented; using the list …
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The Trapped Knight
The Trapped Knight problem is a chess-based problem apparently invented by Neil Sloane and giving rise to a finite number sequence in his Online Encyclopedia of Integer Sequences (OEIS A316667). The squares of an infinite chess board are numbered in a spiral, as in this …
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What N Things?
The mildly controversial geocoding system What3words encodes the geographic coordinates of a location (to a resolution of 3 m) on the Earth's surface into three dictionary words, through some proprietary algorithm. The idea is that humans find it easier to remember and communicate these words …
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Using prime numbers to determine if two words are anagrams
A recent tweet by Fermat's Library noted that the Fundamental theorem of arithmetic provides a novel (if inefficient) way of determining whether two words are anagrams of one another. The Fundamental theorem of arithmetic states that every integer greater than 1 is either a prime …
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Maze Generation by Cellular Automaton
Cellular automata (CA) can be used to generate mazes, as described on the LifeWiki. A commonly used algorithm operates like John Conway's Game of Life in that a cell is born if it has exactly 3 neighbours but the survival rule is more liberal: a …
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Making a maze
The Depth-first search algorithm is a simple approach to generating a maze. It is well described and illustrated in lots of places on the internet, so only an outline is given here. The maze is considered to consist of a grid of cells; each cell …
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Solving word wheels
The Guardian is one of several newspapers which publish a daily "word wheel" puzzle: eight letters are arranged in a circle around a central letter and the goal is to make as many words as possible including the central letter and using each letter once. …