Fun questions, answered
30 short answers from 6 guides. Each set links to the full guide for the worked examples and the reasoning behind the answer.
Classic Browser Games: Rules and Strategies That Actually Work
What is the best strategy for 2048?
The corner chain works for nearly everyone in 2048. Keep your largest tile in one corner, say bottom-left, and mostly press Down and Left, using Right only when needed and Up only when nothing else moves. Keep the bottom row full so it cannot slide, and build a descending chain such as 1024, 512, 256, 128.
How does Wordle handle duplicate letters?
Wordle colours repeated letters in two passes. Exact matches turn green first and use up their letter, then a letter turns yellow only while the answer still has an unused copy. Guessing LLAMA against HOTEL gives one yellow L and one grey L, while against HELLO, which has two Ls, both guessed Ls turn yellow.
What Minesweeper patterns help you avoid guessing?
A few repeating Minesweeper shapes solve most boards. If a number already touches that many flags, its other hidden neighbours are safe. In a 1-2-1 against a wall, mines sit under both 1s and the square under the 2 is safe. In a 1-2-2-1, mines sit under the two 2s. In a 1-1 from an edge, the third square along is safe.
How do you get a high score in Snake?
In Snake, play for space rather than speed. Once the snake is longer than about a third of the board width, stop cutting through the middle and travel in long sweeps along the walls, returning in parallel lanes like mowing a lawn. When the path to the food is not clear, follow your own tail, because that cell is always about to become free.
What Sudoku techniques should beginners learn first?
Most Easy and Medium Sudoku grids fall to four techniques used in order. Cross-hatching follows rows and columns containing a digit through each box to find its only cell. Naked singles fill a cell when eight digits are already taken. Pairs remove two locked candidates from the rest of a unit, and pointing removes a digit from a row when a box confines it there.
Fair Random Decisions: Coin Flips, Wheels, Shuffles and Even Groups
Is a coin flip really 50/50?
A real coin is close to 50/50 but not exactly. A 2007 analysis by Persi Diaconis, Susan Holmes and Richard Montgomery predicted that a flipped coin lands on the side it started on about 51% of the time, and a 2023 study by František Bartoš and colleagues of 350,757 flips measured about 50.8%. The bias favours the starting face, not heads or tails as such.
What is the Fisher-Yates shuffle?
The Fisher-Yates shuffle makes every ordering of a list equally likely. Walk from the last position down and swap each item with a random position at or below it, which gives n! possible swap sequences, exactly one per ordering. Ronald Fisher and Frank Yates described it for pencil and paper in 1938, and Richard Durstenfeld published the in-place computer version in 1964.
What is modulo bias?
Modulo bias is the unfairness that appears when a random number is reduced with %, such as randomByte % 6. Since 256 is 6 times 42 plus 4, the values 0 to 3 each get 43 chances and 4 and 5 only 42, a 2.4% relative tilt. Rejection sampling fixes it by discarding draws above the largest multiple of n and drawing again.
Is Math.random() good enough for a random draw?
Math.random() is a fast pseudo-random generator, xorshift128+ in V8, that is fine for animations and game effects, but its internal state is small and recoverable from a handful of outputs. For draws, tokens and passwords, use crypto.getRandomValues(), which takes bytes from the operating system's cryptographically secure generator, the same source browsers use for TLS keys.
How do I split people into equal teams?
Work out the number of groups first, then share out the remainder so no two groups differ by more than one person. For 10 people in groups of 3, that means 4 groups sized 3, 3, 2 and 2, rather than a naive 3, 3, 3 and 1. Shuffle the names fairly with Fisher-Yates before dealing them into the groups.
How a 3D Web Globe Works: Map Projections, Borders and Country Data
How does a 3D globe wrap a flat map onto a sphere?
A 3D web globe uses an equirectangular image, where longitude runs across the x axis from -180 to +180 and latitude up the y axis from -90 to +90. That maps directly onto the sphere's texture coordinates: u is (longitude + 180) / 360 and v is (latitude + 90) / 180, with no reprojection or lookup table needed.
What is the equirectangular projection?
The equirectangular projection, also called plate carrée, is the simplest map projection: longitude is plotted straight across and latitude straight up, so the image is exactly twice as wide as it is tall. It is the standard globe texture, but it stretches Greenland and Antarctica wide because every row of pixels has the same width.
What is the haversine formula used for?
The haversine formula computes great-circle distance, the distance along the surface of the Earth between two latitude and longitude points, using a mean Earth radius of 6371 km. Because it works with sin(dLng / 2) squared, it wraps around the date line on its own, so a click near Fiji is measured as about 87 km away rather than 359 degrees.
Why are some small countries not clickable on a 3D globe?
Monaco, Vatican City and Tuvalu are too small for the Natural Earth 1:110m polygons. That is the coarsest of Natural Earth's three scales: it keeps files small and a spinning globe smooth, but it simplifies coastlines heavily and drops many small islands.
How accurate are the country facts on a globe?
Globe country facts are written for browsing, so treat them like a good encyclopaedia summary. Capitals and currencies change, as when Kazakhstan's capital went back to Astana in 2022 or Croatia moved to the euro in 2023, and populations are rounded and dated. For anything you will cite, use the UN World Population Prospects or a national statistics office.
How to Solve the 15 Puzzle: A Row-by-Row Method
What was Sam Loyd's 14-15 puzzle?
In 1880 newspapers across the United States printed a 15 puzzle with the 14 and 15 tiles swapped and offered cash to anyone who could put them back in order. Nobody collected, because the position is impossible: in 1879 William Johnson and William Story had proved that exactly half of all 15 puzzle arrangements can never be solved.
How do you check if a sliding puzzle is solvable?
Read the tiles left to right, top to bottom, ignoring the gap, and count inversions: pairs where a bigger number comes before a smaller one. With the gap in the bottom-right corner, a sliding puzzle is solvable when the inversion count is even. On an even-width board with the gap in row r from the bottom, inversions + r must be odd.
How do you place the last tile in a row of the 15 puzzle?
Place the last two tiles of a row as a pair, because placing them one at a time pushes the first out of its corner. For the top row, put 4 in position 3 and 3 directly below it, bring the gap to the top-right corner, then slide 4 right and 3 up. The second row uses the same pair park with 7 and 8.
How do you solve the last two rows of the 15 puzzle?
Solve the bottom two rows of the 15 puzzle as columns from the left, again in pairs. Put 13 in position 9 and 9 directly to its right, bring the gap to the bottom-left corner, then slide 13 down and 9 left. Do the same for 10 and 14, then rotate 11, 12 and 15 around the last 2 by 2 square.
How do you solve bigger sliding puzzles like 5 by 5?
Bigger sliding puzzles use the same method as the 4 by 4: solve rows from the top until two remain, then solve the last two rows as columns from the left. Each solved row or column turns the puzzle into a smaller one, so a 6 by 6 becomes a 4 by 4 after two rows and two columns.
Playing Piano on a Computer Keyboard: Note Names, Keys and First Songs
What frequency is middle C?
Middle C, C4, is about 261.63 Hz in twelve-tone equal temperament with A4 at 440 Hz. The formula is f = 440 × 2^(n/12), where n is the number of semitones from A4, and C4 is 9 semitones below it. C5, one octave higher, is 523.25 Hz, because each octave doubles the frequency.
Why is A4 tuned to 440 Hz?
Concert pitch, fixed by the ISO 16 standard, sets A4 at 440 Hz. Every other note follows from twelve-tone equal temperament: an octave doubles the frequency and is split into 12 equal semitones, so each step multiplies the frequency by the twelfth root of 2, about 1.05946. In MIDI numbering, A4 is note 69 and middle C is 60.
What are the computer keyboard notes for Happy Birthday?
On a QWERTY computer keyboard piano where A is middle C, Happy Birthday in F major is A A S A F D, then A A S A G F, then A A K H F D S, then U U H F G F. The U key is the black key B-flat. The third line, with the jump up to K, is the "Happy birthday, dear Sam" line.
Is the Happy Birthday song in the public domain?
Happy Birthday has been treated as public domain in the United States since a 2016 settlement, after a US court ruled in 2015 that the long-claimed copyright on the lyrics was not valid. The tune itself is old: it started as "Good Morning to All" by Mildred and Patty Hill in 1893.
Why do piano octave numbers change at C instead of A?
In scientific pitch notation, octave numbers tick over at C, not at A, so B3 is directly below middle C (C4) and A4 is above it. That catches many beginners. A note name like C#4 combines the letter, the accidental, where # is one semitone up, and the octave number, so C#4 and Db4 are the same key.
Small Screen Breaks That Help: Confetti, Jokes, Fortunes and Calm Activities
Why does the online fortune cookie stay the same all day?
The Online Fortune Cookie joins your public IP address with today's date in your local time zone, runs a 32-bit string hash over that and takes the remainder after dividing by the number of fortunes, about 470. The same input always gives the same fortune, so refreshing changes nothing until tomorrow, while a VPN changes your IP and therefore your fortune.
What is attention restoration theory?
Attention restoration is research that Rachel and Stephen Kaplan began in the 1980s. It separates directed attention, the effortful focus used to debug or write, from soft fascination, the easy, involuntary interest of watching water or a fire. Directed attention tires and soft fascination lets it recover, so a good break is low effort and not another feed to scroll.
Why do programmers mix up Christmas and Halloween?
Because Oct 31 == Dec 25. The programming joke works because it is technically true: 31 in octal is 3 x 8 + 1, which is 25 in decimal. Like most programming jokes, it is a pun that swaps one meaning of a word for another, so it only lands with people who know what octal is.
Where did fortune cookies come from?
Fortune cookies are usually traced to Japanese-American bakeries in California in the early 1900s, adapted from a cracker made in Kyoto. Only later did they become a fixture of Chinese restaurants in the United States, which is where most people now associate them.
How do I use a breathing animation to slow my breathing?
Breath Sync in Mindless Activities for Stress Relief shows a circle that grows and shrinks on a 4-second cycle. If that feels fast, breathe in over one full cycle and out over the next, which gives seven or eight slow breaths a minute. It is a break, not treatment, so lasting anxiety or low mood is worth raising with a doctor.