A shingoki book punishes a bad file in a way a sample puzzle never shows. Your buyer judges puzzle forty-one, when the black circle marked 4 turns out to need arms of 3 and 2, or the white circle marked 5 sits on a straight run that is six cells long no matter how it is read, and the solver who trusted the signals concludes the fault is theirs. Shingoki looks gentle: a grid of empty cells, a scatter of black and white circles, and a small number inside every circle. The name is the Japanese word for a traffic signal, and the puzzle behaves like one: the solver draws a single loop, through the centres of cells, horizontally and vertically, passing through every circle β going straight through each white circle, turning at each black circle β and the number in a circle is the total length of the two straight segments that meet there, the distance from that circle to where the loop next turns, added across both arms. It is a contract in five parts, each part exact. First, the loop rule: one single, non-intersecting loop, no branches, no crossings, no cell visited twice, and the loop passes through every circled cell. Second, the white rule: at a white circle the loop goes straight β it enters from one side and leaves by the opposite side, never turning in that cell. Third, the black rule: at a black circle the loop turns β it enters from one side and leaves by an adjacent side, a right angle in that cell. Fourth, the number rule: the number in every circle, black or white, is the sum of the lengths of the two segments that meet at that circle, each length measured to the cell where the loop next turns. Fifth, tying it shut: exactly one loop, reachable by deduction alone, with no guessing. A puzzle that breaks any part is not slightly harder. It is false as stated. A good shingoki book is a verified loop: every circle re-measured from its own key, arm by arm, puzzle by puzzle.
Two warnings belong at the front, because they are the mistakes this genre makes most often, and both start with puzzles shingoki is not. Shingoki is not masyu. Masyu uses the same black and white circles and the same single loop, and a buyer who has solved masyu will open your book expecting masyu's extra conditions β that the loop turns in a cell next to a white circle, and runs straight through the cells next to a black one. Shingoki has neither condition. Its white circles say only "straight here", its black circles say only "turn here", and what masyu leaves to position, shingoki replaces with arithmetic: every circle is numbered, which masyu circles never are. A book, a listing, or a rules page that borrows masyu language teaches the buyer a puzzle the pages do not contain. Shingoki is not balance loop either: there is no rule that a white circle's arms are equal or a black circle's arms unequal β colour fixes turning, never proportion. The second warning is what the number means, because it is misread in both directions. The number is the sum of the two arms, not the length of each arm, and not the length of the longer arm: a black 4 can be 3 and 1, or 2 and 2, or 1 and 3, and deciding which is the solving. And a sum is only checkable under a stated counting convention β whether a segment's length counts the cells it runs through, the steps between cells, or the distance to the turning cell β so a serious book states its convention in words, shows it on one worked example where a reader can count both arms and watch them add to the printed number, and audits every key with that same convention. A setter who generated puzzles under one convention and wrote the rules page under another has shipped a book in which every number looks wrong.
The book is the loop, not the sample puzzle
Buyers do not buy a circle style. They buy the promise that every puzzle in the file obeys the rules printed at the front, at the difficulty the cover claims, in the order the book presents them. A free sample almost never breaks that promise, because a sample is the one puzzle the setter checked three times. The breakage lives at puzzle forty-one, in the middle of the book, where a generator exported the grid from one loop and the key from the next, or a hand-setter moved a circle one cell to fix a corner, quietly changed every arm that circle owned, and never re-measured a single sum. That is why the unit of quality in a puzzle book is the whole set, verified as a set: the same checks, run the same mechanical way, on every single puzzle, with the results kept. If you generated the puzzles, keep the generator's settings per puzzle, including its counting convention. If you set them by hand, keep your solving notes. When a buyer writes in about one puzzle β and in this genre they write in with the page number and the circle they cannot make add up β you want to answer about that puzzle, not go hunting through a file you can no longer reconstruct.
The rules page is part of the product, not decoration. State all five parts of the contract in plain language, with one small worked example showing a short loop being traced circle by circle: one black circle whose two arms are counted out loud and added to its printed number, one white circle whose straight run is measured in both directions to its two turns, and the loop closing with every circle visited. That worked example is the one idea a new buyer must carry away, because shingoki is solved against the sums, not just against the shapes, and it is the idea a short rules page most often drops in favour of a pretty picture of a finished loop with no arm ever counted. Most one-star reviews in this genre are not "too hard" or "too easy". They are "the numbers do not work" β and that mismatch is almost always a setter who held the real loop in their head, or in the generator, and printed circles that were never re-measured from their own key.
The contract, part by part
The loop rule is the frame everything else hangs on, so check it like one. The finished drawing is a single closed loop: it never crosses itself, never branches, never passes through the same cell twice, and it passes through every circled cell β a loop that skips a circle, however elegant, has not solved the puzzle, and a second small loop hiding in a corner is not a stylistic choice, it is a second solution component that invalidates the first. Audit the key as a path, not as a picture: trace it from any cell, count the circled cells it visits, and confirm you return to the start having visited every circle and every loop cell exactly once.
The colour rules are where the loop's shape is decided, and they admit no exceptions. At every white circle the key must run straight β a key that bends at a white circle, even once, even in a corner where a bend looks forced, is a broken key. At every black circle the key must turn β a key that runs straight through a black circle is equally broken. These two checks are purely local, purely mechanical, and catch a whole class of generator and transcription errors before any arithmetic is done: extract every circled cell from the printed grid, look up that cell in the key, and record straight or turn against its colour, one line per circle, no sampling.
The number rule is the part solvers actually solve with, and the part keys most often get wrong. For each circle, follow the key's loop in both directions from that cell until it next turns; measure each arm under the book's stated convention; add them; compare with the printed number. The arms of neighbouring circles overlap β one circle's arm can run through another circle's cell, and a segment can serve two sums at once β which is exactly why a single moved circle or a single re-routed segment corrupts several numbers at a time, and why the audit must be exhaustive rather than spot-checked. A wrong sum does double damage: it is wrong itself, and it makes the deductions that depend on the true split impossible, so the buyer stalls several moves earlier than the error and blames the wrong step.
Uniqueness is the part of the contract a plausible loop cannot promise. A grid can usually carry more than one colour-respecting, sum-respecting loop if the setter only checks that a loop exists β long straight corridors and symmetric circle placements are where second loops hide β and a puzzle that loops two ways tells one of its two correct solvers they are wrong. The fifth part therefore has to be proven, not assumed: an independent solve, or a solver run, that counts loops and returns exactly one, with that one reachable by deduction rather than by trying a split both ways until one branch survives.
Verification: re-measure every arm, then count the loops
Verification is a separate pass from solving, done mechanically, ideally by a different method than the one that made the puzzle. Solve each puzzle once as a buyer would, by deduction only, and keep the solve honest: if you guessed a split, and the guess worked, that puzzle has not been shown to have one solution, and it goes back. Then run the structural audit on the key, in this order. One: inventory audit β every circle on the puzzle page appears on the key page, in the same cell, with the same colour and the same number. Two: loop audit β the key is one single loop, traced end to end, visiting every circled cell exactly once, with no branches, crossings, or separate components. Three: colour audit β the key runs straight at every white circle and turns at every black circle, checked cell by cell, no exceptions. Four: arm audit β for every circle, both arms are re-measured from the key to their next turns under the stated counting convention. Five: sum audit β the two re-measured arms add to the printed number for every circle, black and white alike. Six: split audit β at the start of the solve, at least one circle's sum has only one feasible split given the grid edges and neighbouring turns, so the buyer has an honest first move that is a deduction, not a coin flip. Seven: uniqueness audit β a second, independent solve, or a solver run, that counts loops and returns exactly one. Eight: consistency β puzzle page, key page and any thumbnail or marketing sample of that puzzle are the same puzzle, with the same circles in the same cells and the same numbers in the same circles.
Keep the audit results with the book's files, puzzle by puzzle. When a corrected edition ships, that record is how you know which puzzles actually changed and which were only suspected. It is also how you answer the buyer who found a real error: not with an apology and a shrug, but with the corrected puzzle, the audit lines that now pass, and the corrected file sent to everyone who bought the book β which is where the delivery side of this business, covered below, stops being administration and becomes the difference between a one-star review and a loyal repeat buyer.
Difficulty is split pressure and arm overlap, not just grid size
Grid size is the weakest difficulty lever in shingoki, and the one covers lean on hardest. A large grid whose circles carry small sums, with arms that turn quickly and splits that are forced by the edges, falls circle by circle in a satisfying chain, while a small grid whose circles carry large sums with several feasible splits each, overlapping along the same corridors, can stop an experienced solver cold. The real levers are these. Split pressure: how many ways each printed sum can divide into two arm lengths, and how many of those divisions the surrounding geometry rules out before any solving starts β a 4 that can only be 3-and-1 near an edge is a gift, a 9 in open space is a commitment problem. Arm overlap: arms that run through other circles bind the sums together, so one deduction settles several circles at once β or one mistake corrupts them together β and a book can be graded by how tightly its sums are coupled. Turn density: black circles fix the loop's corners, so their number and spacing decide how much of the loop's shape is given before arithmetic starts; white circles fix its corridors the same way. Corridor length: long runs between turns make individual arms long, sums large, and splits ambiguous, which is real difficulty β but only when the book says that is the game, rather than letting length creep up unmeasured.
Grade a book by testing solves, not by measuring grids. Time honest solves across the set, note where each puzzle's deductions stall and restart, and order the book so difficulty genuinely climbs β early puzzles with small sums, edge-forced splits and generous turn density, later puzzles with large central sums, overlapping arms and splits that only resolve near the end. Print the grading honestly: "easy" should mean the splits mostly force themselves, not merely that the grid is small. A buyer who trusts your grading buys the next volume; a buyer who was ambushed by a three-way split knot on page three of the easy book leaves a review about that instead.
Print honesty: the page is the interface
A shingoki page is read in pencil first and pen last, and the print has to survive both β starting with its circles, because black, white and number together are this genre's most fragile surface. A black circle must read as unmistakably black and a white circle as unmistakably white in greyscale, after a photocopy, at arm's length: a mid-grey fill that photocopies dark will turn white circles into black ones on the copied page, reversing the rule at that cell and making the puzzle unsolvable as printed. The number inside a black circle must print in white, or in a cut-out, with enough contrast to read without zooming β a black digit on a black circle is a missing clue, not a hard one β and digits must be unmistakable in the typeface you choose, 6 never 9 even when the page is turned, because loops are traced from every direction. Your key must print the finished loop boldly, with the circles and their numbers still visible under it, so a buyer can re-measure any arm in the key and check its sum against the printed number instead of taking the picture on faith.
Proof the final PDF, not the working file. Export at the exact trim size, print one puzzle and its key on a home printer at 100 percent, and solve the printed puzzle with the printed rules page as your only reference. Check the three things screens hide: whether black and white circles still read as opposite colours after the page has been photocopied once β classrooms and care settings will photocopy it β whether the numbers inside black circles survive that same copy, and whether there is room in or beside each cell for the small arm-length tallies solvers actually write. If a puzzle needs a screen's zoom to tell a straight signal from a turning one, it is not ready to be a download.
Licensing, provenance, and the download itself
State the licence where the buyer decides, not buried after purchase: who may solve the puzzles (one person, a household, a classroom, a club, a care setting), how many copies they may print, whether a teacher may hand a page to thirty students, whether a club may run one puzzle as a group activity, and whether the file itself may be shared, resold or republished β and say plainly that sharing the file is not the same as sharing a printed page. Puzzle books are bought heavily by teachers, club organisers and carers, and those buyers are trying to comply; a licence they cannot find reads to them as a licence that says no. Say how the book was made, too: hand-set, software-generated and hand-checked, or software-generated and mechanically audited β and state the counting convention your sums use, in the book and in the listing, because a buyer raised on a different convention will otherwise judge your correct puzzles as wrong ones. Provenance is not an apology β in this genre it is a quality claim, as long as it is specific. "Generated, then every arm of every circle re-measured from its own key, and every puzzle proven to have exactly one loop" is a claim a buyer can weigh; "high quality puzzles" is not.
Delivery is the last part of the contract. The buyer should get the file immediately, from a link that works the first time, on the device they bought it on, with re-downloads available when β not if β they lose it. Send a corrected edition to every past buyer when one ships; do not wait for them to discover the errata the hard way. I run my own download delivery through FileFreight β flat monthly pricing instead of a cut of every sale, expiring links, and updated files reaching past buyers without me re-emailing attachments by hand β but whatever you use, test it as a buyer: pay, receive, download, lose the file, recover it, and receive an update, before you ask strangers to trust it with money.
The launch checklist
- Every puzzle solved by deduction alone β no guessed split in any solve, start to finish.
- Colour audit passed: the key runs straight at every white circle and turns at every black circle, on puzzle pages and key pages alike.
- Sum audit passed: both arms of every circle, re-measured under the stated counting convention, add to its printed number.
- Loop audit passed: the key is a single loop visiting every circled cell exactly once, with no branches, crossings or separate components.
- Uniqueness audit passed: exactly one loop satisfies the colour, sum and loop rules, and it is the loop printed in the key.
- Print proof passed: black and white circles unmistakable after one photocopy, numbers legible inside black circles, on a home-printed page at final size.
- The errata rule honoured in advance: any circle whose arms do not sum to its number, any bend at a white circle or straight pass at a black one in the key, any second loop or any forced guess means a corrected file goes to every buyer, not just the one who noticed.
