https://laborilo.com/guides/ Plain-language explainers on the ideas behind Laborilo's free browser tools. en Sun, 30 Aug 2026 15:24:21 GMT https://laborilo.com/guides/why-word-counts-vary-between-tools/ https://laborilo.com/guides/why-word-counts-vary-between-tools/ Paste the same paragraph into two different word counters and you can get two different numbers. Here's why "word," "page," and "reading time" are all softer definitions than they sound. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-we-still-memorize-times-tables/ https://laborilo.com/guides/why-we-still-memorize-times-tables/ Multiplication tables are one of the oldest surviving pieces of math education, dating to Babylonian clay tablets. And cognitive science has a specific reason schools haven't dropped them. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-sudoku-puzzles-need-17-clues/ https://laborilo.com/guides/why-sudoku-puzzles-need-17-clues/ In 2012, a supercomputer proved something Sudoku setters had only suspected for decades: no 16-clue puzzle can ever have exactly one solution. Here's why. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-substituted-passwords-are-weak/ https://laborilo.com/guides/why-substituted-passwords-are-weak/ Swapping letters for symbols feels clever, but password-cracking tools check exactly those substitutions first, as a standard, automated step. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-stacked-discounts-dont-add-up/ https://laborilo.com/guides/why-stacked-discounts-dont-add-up/ Sequential discounts multiply, they don't add. Here's the actual math behind stacked sale signage, and why it always looks bigger than it is. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-ssa-triangles-can-have-two-answers/ https://laborilo.com/guides/why-ssa-triangles-can-have-two-answers/ Enter two sides and a non-included angle and a triangle solver can hand back two genuinely different, equally correct triangles. Here's why the 'ambiguous case' exists and how to avoid it. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-gpa-scales-dont-compare/ https://laborilo.com/guides/why-gpa-scales-dont-compare/ A 4.0 GPA doesn't mean the same thing everywhere. Weighted scales, grade inflation, and international differences all break the comparison. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-few-babies-arrive-on-due-date/ https://laborilo.com/guides/why-few-babies-arrive-on-due-date/ A due date is a single-point estimate from a formula nearly two centuries old. Real gestation length varies enough that hitting it exactly is the exception, not the rule. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-designers-use-nonsense-placeholder-text/ https://laborilo.com/guides/why-designers-use-nonsense-placeholder-text/ Placeholder text is deliberately meaningless, and that's the point. Eye-tracking research on how people actually read explains why real words get in a designer's way. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-date-math-is-hard/ https://laborilo.com/guides/why-date-math-is-hard/ Leap years, timezone boundaries, and a 1582 calendar reform still trip up date arithmetic today. Here's what's actually going on under a "days between two dates" calculation. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-computers-use-binary/ https://laborilo.com/guides/why-computers-use-binary/ A 1703 essay on binary arithmetic, an early decimal computer that lost out, and a hugely influential master's thesis explain why every computer counts in two digits. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-calorie-counts-are-approximate/ https://laborilo.com/guides/why-calorie-counts-are-approximate/ Nutrition labels can legally be off by a wide margin, and the underlying formula is 130 years old. Here's what a calorie count actually represents. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/why-base64-makes-files-bigger/ https://laborilo.com/guides/why-base64-makes-files-bigger/ Base64 encoding reliably inflates file size by about 33%, and the reason it exists at all traces back to 7-bit email transport from the early internet. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/where-tipping-culture-came-from/ https://laborilo.com/guides/where-tipping-culture-came-from/ American tipping wasn't always normal. It was once considered un-American and banned in several states. Here's the actual history. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/what-wpm-actually-measures/ https://laborilo.com/guides/what-wpm-actually-measures/ A "word" in a typing test isn't a word. It's a fixed 5-character unit. Here's how WPM is actually calculated, and what it doesn't tell you about real typing. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/what-moves-exchange-rates/ https://laborilo.com/guides/what-moves-exchange-rates/ Exchange rates move on interest rate differences, inflation, trade flows, and central bank action. Here's how each one pushes a currency up or down, in plain terms. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/what-bmi-actually-measures/ https://laborilo.com/guides/what-bmi-actually-measures/ BMI was never designed as a personal health metric. Here's where the formula came from, what it's actually good for, and which measurements fill in the gaps it leaves. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/what-a-hash-actually-guarantees/ https://laborilo.com/guides/what-a-hash-actually-guarantees/ Hashing isn't encryption, and "decrypting a hash" is a category error. Here's what a cryptographic hash actually promises, and what MD5's real, documented weakness is. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/wcag-contrast-ratios-explained/ https://laborilo.com/guides/wcag-contrast-ratios-explained/ Where the WCAG contrast ratio formula comes from, why 4.5:1 became the readability threshold, and what it doesn't check for. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/unix-time-timezones-leap-seconds/ https://laborilo.com/guides/unix-time-timezones-leap-seconds/ Unix timestamps count seconds since 1970 and deliberately ignore leap seconds. Here's why that shortcut exists, and why the world is retiring leap seconds by 2035. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/true-randomness-vs-pseudorandom/ https://laborilo.com/guides/true-randomness-vs-pseudorandom/ Most software "randomness" is a deterministic algorithm in disguise. Here's the real difference between a PRNG and genuine unpredictability. And a famous case where the gap mattered. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/the-origin-story-of-json/ https://laborilo.com/guides/the-origin-story-of-json/ Douglas Crockford says he didn't invent JSON so much as notice it was already hiding inside JavaScript's own syntax. Here's how a format with no official inventor took over the web. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/screen-recording-codecs-explained/ https://laborilo.com/guides/screen-recording-codecs-explained/ Two recordings of the same length and resolution can differ in size by 10x depending on codec and content. Here's what's actually driving the difference. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/science-behind-the-pomodoro-technique/ https://laborilo.com/guides/science-behind-the-pomodoro-technique/ Francesco Cirillo picked 25 minutes because it felt manageable, not because a study proved it optimal. Here's what's actually backed by research and what's folklore. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/sales-tax-vs-vat/ https://laborilo.com/guides/sales-tax-vs-vat/ Over 170 countries run on value-added tax. The US never adopted it, and instead ended up with thousands of overlapping local sales-tax rates. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/rule-of-72-compound-interest/ https://laborilo.com/guides/rule-of-72-compound-interest/ A quick mental-math trick estimates how long money takes to double. And explains why compounding always feels like it's doing nothing, until suddenly it isn't. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/regular-expressions-history/ https://laborilo.com/guides/regular-expressions-history/ Regex started as 1950s mathematical logic, decades before it became a programming tool. And grep's very name is a fossil of how it got there. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/percentage-points-vs-percent-change/ https://laborilo.com/guides/percentage-points-vs-percent-change/ Going from 5% to 10% is a 5-point increase and a 100% increase. Here's the difference, and why finance uses basis points to avoid it entirely. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/password-strength-length-vs-complexity/ https://laborilo.com/guides/password-strength-length-vs-complexity/ Why the security world walked away from 'P@ssw0rd!' style complexity rules, what NIST actually recommends now, and the math behind why a longer passphrase beats a short jumble of symbols. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/lossy-vs-lossless-compression/ https://laborilo.com/guides/lossy-vs-lossless-compression/ JPEG throws away image data your eye is bad at noticing; PNG throws away nothing. Here's what each approach actually does to the pixels, and when the tradeoff is worth it. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/how-spreadsheet-data-gets-corrupted/ https://laborilo.com/guides/how-spreadsheet-data-gets-corrupted/ A gene-naming standards body renamed human genes because Excel kept turning them into dates. Here's why plain-text table formats break more often than they should. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/how-qr-codes-survive-damage/ https://laborilo.com/guides/how-qr-codes-survive-damage/ A QR code can lose up to 30% of its data and still scan. The error-correction math behind that, and why some codes can have a logo stamped in the middle. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/how-mortgage-amortization-works/ https://laborilo.com/guides/how-mortgage-amortization-works/ Your first mortgage payment and your last one are the same size but almost nothing alike. Here's why early payments are mostly interest, and how extra principal payments actually save you money. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/how-diff-algorithms-work/ https://laborilo.com/guides/how-diff-algorithms-work/ The Myers algorithm behind git diff and most text-comparison tools, explained without the computer-science notation, and why two people can get two different "correct" diffs from the same input. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/how-browsers-throttle-background-timers/ https://laborilo.com/guides/how-browsers-throttle-background-timers/ Browsers deliberately slow down JavaScript timers in tabs you're not looking at. Here's why a countdown can "jump" when you switch back, and how it's supposed to self-correct. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/gross-pay-vs-net-pay/ https://laborilo.com/guides/gross-pay-vs-net-pay/ The number in your job offer and the number that hits your bank account are rarely the same. Here's the deduction stack that explains the gap. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/costly-unit-conversion-mistakes/ https://laborilo.com/guides/costly-unit-conversion-mistakes/ A $125 million spacecraft and a passenger jet that ran out of fuel mid-flight both trace back to unit conversion errors. Two real cases, and why the US still hasn't fully gone metric. Thu, 20 Aug 2026 00:00:00 GMT https://laborilo.com/guides/camelcase-vs-snake-case-history/ https://laborilo.com/guides/camelcase-vs-snake-case-history/ Naming conventions trace back to Smalltalk, PEP 8, and early terminal limitations. Inherited history, not a technical requirement. 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