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Make a free printable Christmas word search in seconds. Grab a ready-to-use holiday word list, difficulty tips, and a free puzzle maker that builds unique.

Make a free printable Halloween word search in seconds. Grab a spooky ready-to-use word list, difficulty tips, and a free puzzle maker that builds unique grids.

Make a free printable Thanksgiving word search in seconds. Grab a ready-to-use fall word list, difficulty tips, and a free puzzle maker that builds unique.

Make a free printable Easter word search in seconds. Grab a ready-to-use spring word list, difficulty tips, and a free puzzle maker that builds unique grids.

Make a free printable Valentine's Day word search in seconds. Grab a ready-to-use love word list, difficulty tips, and a free puzzle maker that builds unique.

Make a free St. Patrick's Day word search in seconds. Grab a ready-made word list, classroom tips, and a tool that builds printable puzzles for any age.

Make a free New Year word search in seconds. Get a ready-made word list, party tips, and a tool that builds printable puzzles for kids and adults.

Make a free 4th of July word search in seconds. Get a ready-made word list, BBQ party tips, and a tool that builds printable puzzles for all ages.

Make a free winter word search in seconds. Get a ready-made word list, classroom tips, and a tool that builds printable puzzles for kids and adults.

Make a free fall word search in seconds. Get a ready-made autumn word list, classroom tips, and a tool that builds printable puzzles for all ages.

Make a free spring word search in seconds. Grab a ready-to-use word list, age-by-age tips, and a free puzzle maker that prints clean, custom grids fast.

Make a free summer word search in seconds. Grab a ready-to-use word list, age-by-age tips, and a free puzzle maker that prints clean, custom grids fast.

Make a free animals word search in seconds. Grab a ready-to-use word list, age-by-age tips, and a free puzzle maker that prints clean, custom grids fast.

Make a free planets & space word search in seconds. Grab a ready-to-use word list, age-by-age tips, and a free puzzle maker that prints clean grids fast.

Make a free US presidents word search in seconds. Grab a ready-to-use word list, age-by-age tips, and a free puzzle maker that prints clean grids fast.

Make a free states & capitals word search in seconds. Grab a ready-to-use word list, classroom tips, and a generator that prints unique geography puzzles.

Make a free human body word search in seconds. Grab a copy-and-paste word list of organs and bones, science teaching tips, and a printable puzzle generator.

Make a free dinosaurs word search in seconds. Grab a copy-and-paste list of dinosaur names, party and classroom tips, and a printable puzzle generator.

Make a free ocean animals word search in seconds. Grab a copy-and-paste sea creature word list, classroom tips, and a printable puzzle maker. No sign-up.

Make a free weather word search in seconds. Grab a copy-and-paste weather word list, science teaching tips, and a printable puzzle maker. No sign-up needed.

Make a free insects word search in seconds. Grab a ready-made bug word list, difficulty tips by age, and a free puzzle maker that prints unique copies.

Make a free plants word search in seconds. Grab a ready-made nature word list, age-by-difficulty tips, and a free puzzle maker that prints unique copies.

Make a free periodic table word search in seconds. Grab a ready-made element word list, difficulty tips, and a free puzzle maker that prints unique copies.

Make a free countries word search in seconds. Grab a ready-made country word list, difficulty tips by age, and a free puzzle maker that prints unique copies.

Make a free Spanish word search in seconds. Grab a ready-made Spanish word list, difficulty tips by level, and a free puzzle maker that prints unique copies.

Make a free printable French word search in seconds. Grab ready-to-use French word lists by theme, plus printing tips and a free puzzle maker for any class.

Make a free printable sight words word search fast. Grab Dolch and Fry word lists by grade, plus printing tips and a free puzzle maker for any classroom.

Turn any spelling list into a free printable word search in seconds. Grab grade-level word lists, printing tips, and a free puzzle maker for spelling practice.

Make a free printable SAT vocabulary word search in seconds. Grab a high-frequency SAT word list with definitions, study tips, and a free puzzle maker.

Make a free, easy kindergarten word search in seconds. Grab simple themed word lists, age-perfect settings, and a free puzzle maker for little learners.

Make a free 1st-2nd grade word search in seconds. Grab age-perfect word lists, printing tips, and a tool that builds easy, kid-friendly puzzles to print.

Make a free 3rd-5th grade word search in minutes. Get ready-to-use word lists, difficulty tips, and a tool that builds printable puzzles for upper grades.

Make a free middle school word search in minutes. Grab subject word lists, difficulty tips, and a tool that builds challenging printable puzzles fast.

Make a free hard word search for adults in minutes. Get challenging word lists, difficulty tips, and a tool that builds big, printable expert puzzles.

Make a free birthday word search in minutes. Grab a party word list, age tips, and a tool that builds printable puzzles for goody bags and party tables.

Make a free baby shower word search in seconds. Grab a ready-made word list, printing tips, difficulty levels, and a free puzzle maker for your whole party.

Make a free wedding word search in minutes. Grab a ready-made word list, reception ideas, difficulty levels, and a free puzzle maker for your guests and tables.

Make a free retirement word search in minutes. Grab a ready-made word list, party ideas, difficulty levels, and a free puzzle maker for the guest of honor.

Make a free sports word search in minutes. Grab a ready-made word list, classroom and party ideas, difficulty levels, and a free puzzle maker for any team.

Make a free music word search in minutes. Grab a ready-made word list, classroom and party ideas, difficulty levels, and a free puzzle maker for any music fan.

Make a free movies word search in seconds. Grab a ready-to-use word list, printing tips, and a free puzzle maker that builds unique printable puzzles fast.

Make a free food word search in seconds. Grab a ready-to-use word list, printing tips, and a free puzzle maker that builds unique printable puzzles fast.

Make a free animals for kids word search in seconds. Grab a ready-to-use word list, age tips, and a free puzzle maker that builds printable puzzles in a click.

Make a free back to school word search in seconds. Grab a ready-to-use word list, classroom tips, and a free puzzle maker that builds printable puzzles fast.

Make a free summer camp word search in seconds. Grab a ready-to-use word list, counselor tips, and a free puzzle maker that builds printable puzzles fast.

Make a free easy crossword in seconds. Grab a ready-made word list, beginner tips, and a printable puzzle maker that builds simple crosswords for any group.

Make a free kids crossword in minutes. Grab a ready-made word list, age-by-age tips, and a printable puzzle maker that builds fun, simple puzzles for kids.

Make a free Christmas crossword in minutes. Grab a ready-made holiday word list, fun clues, and a printable puzzle maker for your party, class, or family.

Make a free Halloween crossword in minutes. Grab a ready-made spooky word list, fun clues, and a printable puzzle maker for your party or class party.

Make a free Bible crossword in minutes. Grab a ready-made scripture word list, clue ideas, and a printable puzzle maker for Sunday school, youth group, or home.

Make a free printable music crossword in minutes. Grab a ready-to-use music word list, clue ideas, difficulty tips, and a free puzzle maker that builds your.

Make a free printable sports crossword fast. Grab a ready-to-use sports word list, clue ideas, difficulty tips, and a free puzzle maker that builds the grid.

Make a free printable science crossword fast. Grab a ready-to-use science word list, clue ideas, difficulty tips, and a free puzzle maker that builds the.

Make a free printable vocabulary crossword fast. Turn any word list into a grid with clues and an answer key using a free puzzle maker. Great for any grade.

Make a free printable Spanish crossword fast. Grab a ready-to-use Spanish word list, clue ideas, difficulty tips, and a free puzzle maker that builds the.

Build a free history crossword in minutes. Grab a ready-made clue list, difficulty tips by age, and a printable puzzle maker that turns your words into a.

Make a free math crossword in minutes. Grab a ready-made vocabulary list, difficulty tips by grade, and a printable puzzle maker that turns your terms into a.

Make a free animal crossword in minutes. Grab a ready-made word list, difficulty tips by age, and a printable puzzle maker that turns your animals into a.

Make a free movie crossword in minutes. Grab a ready-made word list, theme ideas, and a printable puzzle maker that turns your film clues into a clean.

Make a free geography crossword in minutes. Grab a ready-made word list, difficulty tips by grade, and a printable puzzle maker that turns your terms into a.

Make a free Thanksgiving crossword in minutes. Grab a ready-made word list, easy clue ideas, and a printable puzzle maker for your class, party, or family.

Make a free Easter crossword in minutes. Grab a ready-made spring word list, easy clue ideas, and a printable puzzle maker for your class, party, or family.

Make a free body parts crossword in minutes. Grab a ready-made word list, clue ideas, and a printable puzzle maker for science class, ESL lessons, or.

Make a free food crossword in minutes. Grab a ready-made word list, tasty clue ideas, and a printable puzzle maker for class, ESL lessons, parties, or.

Make a free weather crossword in minutes. Grab a ready-made word list, clue ideas, and a printable puzzle maker for science class, ESL lessons, or a.

Make a free holiday word scramble in seconds. Grab a ready-to-use word list, an answer key, printing tips, and a free puzzle maker for any festive party.

Make a free animal word scramble in seconds. Grab a ready-to-use word list, an answer key, printing tips, and a free puzzle maker for class or home.

Make a free subject word scramble in seconds. Grab ready-to-use word lists for math, science, and more, plus an answer key and a free puzzle maker.

Make printable puzzles fast with a free word jumble maker. Paste any word list, get scrambled words plus an answer key, and print in seconds. No sign-up.

Make printable cryptograms fast with a free cryptogram maker. Turn any quote or word list into a coded puzzle with an answer key. No sign-up, no install.

Explore the best maze maker uses for classrooms, parties, and quiet time. Get printable maze ideas, age tips, and a free puzzle maker to build your own fast.

Make a free Christmas word scramble in minutes. Grab a ready-made holiday word list, answer key tips, and a printable puzzle maker for your party or classroom.

Make a free Halloween word scramble in minutes. Grab a ready-made spooky word list, answer key tips, and a printable puzzle maker for your class or party.

Make a free Thanksgiving word scramble in minutes. Grab a ready-made fall word list, answer key tips, and a printable puzzle maker for class or dinner.

Discover the best anagram solver uses, from word games to teaching and puzzle making. Get tips, examples, and a free puzzle maker to build printable scrambles.

Make free printable puzzles for teachers in minutes. Word searches, crosswords, and word scrambles built from your own vocabulary list. No sign-up, no fee.

Make free printable puzzles for sub plans in minutes. No-prep word searches, crosswords, and scrambles any substitute can hand out. No sign-up, no fee.

Make free printable puzzles for ESL students in minutes. Word searches, crosswords, and scrambles built from your vocabulary list. No sign-up, no fee.

Make free printable puzzles for homeschool in minutes. Word searches, crosswords, and scrambles built from your own lessons. No sign-up, no fee.

Make free printable puzzles for early finishers in minutes. No-prep word searches, crosswords, and scrambles to keep fast students busy. No sign-up, no fee.

Make puzzles for party favors in minutes. Grab a themed word list, packaging tips, and a free tool that prints word searches, crosswords, and scrambles.

Make puzzles for church groups in minutes. Get a Bible-themed word list, lesson tips, and a free tool that prints word searches, crosswords, and scrambles.

Make puzzles for senior brain games fast. Get large-print word lists, accessibility tips, and a free tool that prints word searches, crosswords, and scrambles.

Make puzzles for summer learning fast. Get grade-level word lists, anti-slide tips, and a free tool that prints word searches, crosswords, and scrambles.

Make puzzles for classroom centers fast. Get word lists, rotation tips, and a free tool that prints self-checking word searches, crosswords, and scrambles.

Make free puzzles for birthday parties in minutes. Grab a ready-made word list, age tips, and a free maker that prints word searches, crosswords, and scrambles.

Make free puzzles for wedding showers fast. Get a ready-made word list, hosting tips, and a free maker that prints word searches, crosswords, and scrambles.

Make free puzzles for escape rooms fast. Get a ready-made word list, clever clue ideas, and a free maker that prints word searches, crosswords, and scrambles.

Learn how to make a word search in minutes. A simple step-by-step guide plus a free maker that prints custom word searches with no sign-up and no software.

Learn how to make a crossword in minutes. A clear step-by-step guide plus a free maker that builds custom crosswords with clues, no sign-up and no software.

The word search benefits for kids go far beyond fun. See how puzzles boost spelling, focus, and confidence, plus a free word list and printable maker.

Are puzzles good for the brain? Yes. See how word searches, crosswords, and scrambles boost memory and focus, plus a free word list and printable maker.

Learn how to make puzzles in Word with tables and shapes, plus a faster free way to build printable word searches, crosswords, and scrambles in seconds.

Find the best puzzle difficulty by age with a clear chart for word searches, crosswords, and scrambles, plus a free word list and printable puzzle maker.

Learn how to print puzzles cleanly: best paper, margins, and ink settings for word searches, crosswords, and scrambles, plus a free printable puzzle maker.

Learn how to make an answer key for any word search, crossword, or scramble in minutes. Step-by-step tips plus a free puzzle maker that prints the key for you.

Compared: the best free word search makers in 2026. See which tools print clean grids, add answer keys, and need no sign-up — plus how to make one in seconds.

The best crossword makers in 2026, compared. See which free tools auto-build grids, print clue sheets and answer keys, no sign-up. Make one in seconds.

Looking for Discovery Puzzlemaker alternatives? Compare the best free puzzle makers in 2026 with cleaner grids, answer keys and no sign-up. Make one fast.

The best puzzle makers for teachers in 2026, compared. Free tools that build word searches, crosswords and answer keys with no sign-up. Make a class set fast.

Make free printable crossword puzzles in minutes. Enter words and clues, the grid builds itself, and you print a clean PDF with an answer key. No signup.

Get free sudoku printable puzzles in seconds. Pick Easy, Medium, or Hard, print 1 to 6 per page, and every puzzle has exactly one solution plus an answer key.

Make free word searches printable on any topic. Type your words, pick a grid size and difficulty, and print a clean puzzle with an answer key. No signup.

Get free daily printable crossword puzzles without a subscription. Generate a fresh crossword every morning, print it with an answer key, and build the habit.

Make free printable word searches for adults — big 18x18 grids, diagonal and backwards words, and themes grown-ups enjoy. Print with an answer key, no signup.

Print free easy sudoku puzzles made for beginners. Learn the rules and the two starter techniques, then print 1 to 6 puzzles per page with full answer keys.

Generate free printable mazes in seconds — Easy, Medium, or Hard, with holiday themes and a solution key on its own page. Print as many as you want, no signup.

Make a large print word search printable in seconds. Free maker with big, bold letters, senior-friendly settings, ready word lists, and an answer key.

Make a find a word printable in seconds. Free word find maker with ready word lists, difficulty settings, and an answer key. No sign-up, print instantly.

Print medium printable sudoku free, with unique solutions and answer keys. Learn the solving techniques medium puzzles need and print up to 6 per page.

Print hard sudoku free, each with a unique logic-only solution and answer key. Learn the advanced techniques hard puzzles demand and print up to 6 per page.

Make printable crossword puzzles for adults free. Enter words and clues, get an auto-built numbered grid with an answer key, and print in minutes.

Make mazes for kids printable in one click. Free maze maker with easy to hard sizes, holiday themes, and a solution key. No sign-up, print instantly.

Learn how samurai sudoku printable puzzles work: five overlapping grids, one solve. Get rules, strategy, and free printable sudoku to train on.

Make a blank sudoku printable in minutes: exact steps for clean empty 9x9 grids, the right cell sizes for pencil marks, and free ready-to-solve puzzles too.

Get hard crossword puzzles printable free: learn what makes a crossword genuinely tough, steal our hard clue-writing tricks, and print with an answer key.

Make printable word searches difficult enough for serious solvers: 20x20 grids, all four directions, sneaky word lists, secret messages, and a free answer key.

Get free printable Sunday crossword puzzles: what makes the big weekend grid special, how to build your own themed Sunday-style crossword, and print with a key.

Get hard mazes printable free: generate a fresh challenging maze in one click, learn the strategies that crack tough mazes, and print the solution key too.

Print an easy maze free in seconds — perfect for ages 3 to 7, with one clear path, festive themes, and a solution page. No signup, print as many as you like.

Print a difficult maze free and learn what actually makes mazes hard: branching, false paths, and depth — plus expert solving techniques and a solution key.

Print medium mazes free: the just-right challenge for ages 7-12 and casual adults, one-click generation with a solution key, plus tips for leveling up.

Want 100 hard word search puzzles printable for free? Here's how to generate a full pack in one afternoon — tough settings, 20 theme ideas, and answer keys.

Get a daily sudoku printable free — generate a fresh puzzle every morning, print a week at once, and follow an easy-to-hard weekly ramp with answer keys.

Get free printable sudoku 6 per page — six fresh puzzles on one sheet with answer keys. Perfect for travel packs, classrooms, and homemade puzzle books.

Free printable mazes for adults — generate genuinely hard mazes with answer keys, learn real solving strategies, and use them as a screen-free brain break.

Make easy word search puzzles printable free — gentle settings for young kids, seniors, and ESL learners, plus ready word lists and a step-up difficulty plan.

Make large printable word searches free — full-page 20×20 grids with 30+ words that take a real hour to solve, plus big word lists and print-perfect tips.

Get sudoku difficult printable puzzles free and learn to beat them — the technique ladder from singles to X-Wing, a stuck-grid protocol, and printing tips.

Make a free Halloween maze printable in seconds — spooky start and finish, three difficulty sizes, answer keys, and party ideas for classrooms and handouts.

Make a free Christmas maze printable in seconds. Pick Easy, Medium, or Hard, get a festive start and finish, and print with a solution key. No sign-up.

Get a free printable Valentine's Day word search in minutes. Grade-by-grade word lists, a hidden-message trick, and a print plan for the class party.

Free easy printable crossword puzzles for adults — grown-up words, gentle clues. Copy-paste starter sets, clue-writing tips, and a free maker with answer keys.

Free printable crossword puzzles, medium difficulty — the just-right level. Learn the 70/30 clue formula, grab a starter set, and print with an answer key.

Difficult crossword puzzles printable for free: learn the five misdirection tricks that make clues devious-but-fair, grab a starter set, and print with answers.

Make large print crossword puzzles printable for free. One toggle for big grids and letters, word sets for seniors, and printing tips for low-vision solvers.

Sudoku for beginners, printable and free: the rules in 60 seconds, a first-solve walkthrough, a 4-week practice plan, and Easy puzzles with answer keys.

Get printable crossword puzzles with answers included — every puzzle prints with a completed key on its own page. Free maker, starter set, smart-peek tips.

4x4 sudoku explained - the rules, how it differs from the standard 9x9 grid, and why it

An honest look at the benefits of sudoku — what focus, routine and stress relief it really offers, and why the dementia and IQ claims don't hold up.

A practical childrens sudoku guide — what age to start, the 4x4 to 9x9 progression, how to teach the one rule, and classroom-ready ideas.

Colored sudoku means four different puzzles — colors as symbols, color-coded digits, colored regions, and bead boards. Rules, palettes, and accessibility.

Free printable empty sudoku grids - blank 9x9 boards for building your own puzzles, tracking pencil marks, or teaching the rules from scratch.

What separates extreme sudoku from expert or hard - fewer starting clues, techniques required, and where to play or print extreme puzzles free.

Twelve logic puzzles similar to sudoku, from kakuro and futoshiki to nonograms and slitherlink, with what makes each one different and who will enjoy it most.

Giant sudoku means two things — big printed grids and oversized boards. Every size from 12x12 to 36x36, mega sudoku naming, and Samurai layouts.

What actually makes a sudoku the hardest - the famous contenders, the 17-clue minimum, and why clue count isn

Hexadecimal sudoku explained - a 16x16 grid using 0-9 and A-F, how the rules scale up, and why it

Hexagon sudoku explained: honeycomb boards, three-direction lines, flower regions, symbol sets, and why hexagonal grids feel harder than square ones do.

Learn how to play sudoku from scratch — the three rules, crosshatching, hidden singles, pencil marks, and a fully worked grid you can follow move by move.

Hyper sudoku explained — where the four windows sit, the five hidden regions nobody mentions, a verified grid, and the techniques that solve it.

Jigsaw sudoku replaces the 3x3 boxes with irregular shapes - here

Complete killer sudoku combinations chart with every 2-cell and 3-cell cage sum, the unique combinations for larger cages, and the 45 rule for innies and outies.

Killer sudoku explained — the rules, the rule of 45, full cage combination tables, innies and outies, and a worked solve you can follow step by step.

Letter sudoku explained - the same logic as standard sudoku using letters instead of numbers, plus popular themed versions like word sudoku.

Locked candidate sudoku explained — pointing vs claiming, worked candidate grids with R#C# coordinates, and how to spot both types in under a minute.

How to make your own sudoku puzzle that actually has one valid solution - the process, common mistakes, and easier alternatives.

Mini sudoku compared: 4x4, 5x5 and 6x6 grids, how hard each one really is, who each size suits, and how to pick the right small grid and print it well.

How multiplayer sudoku actually works — same-grid races, relays, team solving, scoring systems, and handicaps that keep mixed-skill groups competitive.

Naked pairs sudoku made simple — what a naked pair is, worked candidate grids with R#C# coordinates, the double-unit bonus, and naked vs hidden pairs.

Skyscraper sudoku explained — two conjugate pairs sharing a base line, worked R#C# examples with eliminations, and why it catches X-wing near-misses.

Free spring-themed sudoku puzzles to print - classroom activities, seasonal decor pages, and a full range of difficulty for any age.

How 12x12 sudoku works: rectangular 4x3 regions, the symbols 1 to 12, why it is harder than a standard 9x9, plus printing tips for free oversized grids.

Play 16x16 sudoku online — the 4x4 box layout, the three symbol sets, a verified solution grid, and the techniques that scale to 256 cells.

An honest guide to sudoku 5x5 — why a 5x5 grid can't have normal boxes, the three puzzles the name actually refers to, and how to solve each one.

Physical sudoku board games explained - how they work, popular versions, and when a physical board actually beats a digital or printed puzzle.

What actually makes a good sudoku book — difficulty progression, grid size, paper, binding, and where the answers go. A buyer's checklist, no brand hype.

How to build a daily sudoku habit using a calendar approach - difficulty pacing across the week, tracking progress, and staying consistent.

A printable sudoku cheat sheet — every technique with its exact trigger and action, plus notation, triage cards and the numbers worth memorizing.

The sudoku diagonal rule explained - both main diagonals must also contain 1-9, adding a powerful extra elimination tool for solvers.

Sudoku evil puzzles need more than scanning. Learn the techniques that crack them: pointing pairs, X-Wing, XY-Wing and coloring.

What a sudoku expert really does differently — chains, uniqueness arguments, mental bookkeeping, timed solving, and where logic actually runs out.

Sudoku VIP 6x6 explained — the real rules of the 6x6 grid, 2x3 boxes, a verified solution, crosshatching on a short grid, and how to solve one fast.

How to get sudoku PDFs that actually print well - grid sizing, puzzles per page, answer keys, and the settings that ruin a print job.

Hidden singles, naked and hidden pairs, triples and pointing pairs - the middle-tier sudoku techniques that crack most hard puzzles.

The real sudoku origin story — Latin squares and Euler, Number Place in Dell in 1979, Nikoli naming it in Japan, and the 2004 newspaper boom.

How to print sudoku with answer keys that are actually usable - where to put solutions, how to number them, and when answers hurt.

The definitive sudoku rules — the single constraint, what counts as a valid puzzle, the myths that aren

The sudoku strategies that matter, ranked by learning order, plus a decision table matching what you see in the grid to the technique that breaks it open.

A real sudoku strategy is an order of operations, not a bag of tricks - here

Practical sudoku tips and tricks for real habits — pencil-mark discipline, scanning order, when to restart, and the beginner errors that cost most.

Sudoku X wing explained with real candidate grids — the 2x2 rectangle rule, why it works, worked row and column examples, and the near-misses to avoid.

Sudoku X-Wing, finned X-Wing, swordfish, and empty rectangle explained clearly, with the pattern to look for and how each one eliminates candidates.

Summer sudoku printables for camp, road trips and the classroom: themed symbol sets, difficulty by age, packet plans, and printing tips that really hold up.

Swordfish sudoku explained: three rows, three columns, one digit. A worked candidate map with R#C# eliminations, and how it differs from an X-wing.

Practical sudoku solving tips that actually work - scanning techniques, pencil marks, and when to use advanced strategies versus guessing.

How the unique rectangle works in sudoku: the deadly pattern logic, all four UR types with worked examples, hidden and avoidable rectangles, and when not to use it.

Candidate mode in sudoku apps explained - what it does, how it differs from regular entry mode, and how to use it effectively.

XY wing sudoku explained clearly — the pivot-and-pincer structure, why it works, three worked examples with real grid positions, and how to find one fast.

Learn the XYZ-Wing sudoku technique step by step: the exact pattern, why the elimination works, worked grid examples, and where the victim cells always hide.

Y wing sudoku explained — it is the same technique as the XY-wing. Pivot, pincers, two worked examples with real R#C# coordinates, and the near-misses.