A Tenner Grid book punishes a bad file in a way a sample puzzle never shows. Your buyer judges puzzle forty-one, when one column sum in the key was added down a draft grid after a late given changed β so the printed foot says 14 under a column whose digits actually add to 17, and no legal placement will ever make that column true β or the sum row shifted one column in export, so every printed total belongs to the column beside it and the whole puzzle reads as almost-solvable nonsense, or a printed 0 in the grid quietly became a blank, deleting a given the whole solve depended on. Tenner Grid β Zehnergitter in its German home tradition β is a digit-placement puzzle played on a grid ten cells wide: every row holds the digits 0 to 9 exactly once, the number printed beneath each column is the sum of the digits in that column, and any two cells that touch, even diagonally, hold different digits. There are no boxes, no cages and no operations: one row rule, one column-sum rule, one touching rule. Underneath that plain surface is a contract in five parts, each part exact. First, the row rule: every row contains each digit from 0 to 9 exactly once β a permutation, never a selection. Second, the column rule: in each of the ten columns, the digits placed β repeats allowed β add up to exactly the number printed beneath that column, no more and no less. Third, the touching rule: digits in cells that touch horizontally, vertically or diagonally must be different, so an equal digit may repeat in a column only with at least one row between its appearances, and in the next row it must also step at least two columns away. Fourth, given integrity: the digits pre-printed in the grid are fixed exactly as published, and a printed 0 is a given like any other β it is never a blank, a placeholder or a printing failure. Fifth, closing the contract, uniqueness: exactly one completed grid satisfies every row, every printed column sum and the touching rule at once, reachable by deduction alone, with no guessing. A puzzle that breaks any part is not slightly harder. It is false as stated. A good Tenner Grid book is a verified set of rows and sums: every column in every puzzle re-added from its own key, column by column, on the final file.
Three warnings belong at the front, because they are the mistakes this genre makes most often, and all three start with puzzles Tenner Grid is not. Tenner Grid is not Sudoku, even though both fill a grid with digits under a no-repeat instinct. Sudoku uses 1 to 9 on a square grid, forbids repeats in columns as strictly as in rows, and adds the box rule. Tenner Grid uses 0 to 9 β ten digits, which is where the name comes from β on a grid ten wide and only a few rows tall, allows repeats down a column, has no boxes at all, and replaces the column's no-repeat rule with an exact sum printed at its foot. A buyer who brings Sudoku habits will read a repeated digit in a column as an error and a column sum as decoration, and both readings are wrong here. Tenner Grid is also not Kakuro, even though both print sums and ask for digits that add to them. A Kakuro clue sums one unbroken run of white cells, no digit may repeat inside that run, the digits are 1 to 9, and the grid is a crossword of runs running in two directions. A Tenner column sum covers the whole column from top row to bottom row, repeats are legal inside it subject to the touching rule, 0 is a working digit, and there is exactly one sum per column, printed once, beneath the grid β never a run, never a split, never a second direction of clues inside the grid. And Tenner Grid is not KenKen, even though both mix placement with arithmetic. A KenKen cage is a bold-outlined group of cells carrying a target and an operation β add, subtract, multiply or divide β and the digits, 1 up to the grid size, repeat in neither row nor column. Tenner Grid has no cages and no operations at all: its only arithmetic is ten plain additions, one per column, and its digits repeat down columns while never repeating across a row. A book must state the standard form plainly β rows as permutations of 0 to 9, one printed sum under every column, touching cells always different β and never let a puzzle generated under a box, run or cage reading slip in unnamed.
The book is the whole set of sums, not the sample puzzle
A sample Tenner Grid almost always behaves. It is usually generously given: enough digits pre-printed that the touching rule fires everywhere at once, and a foot row holding an extreme sum or two β a very small total that forces small digits into that column, a very large one that forces the big digits in β so the grid settles quickly. None of that tests the things a full book can get wrong: one column re-added carelessly from a draft key after a late given moved, so the puzzle on the page is keyed to a grid that no longer exists; a sum row pasted in reverse order, so the totals read left to right underneath a grid whose setter wrote them right to left; a sum of 16 in the key that prints as 10 because a digit was clipped in a tight foot margin, turning a forcing total into one that fits nothing; or a late puzzle whose printed sums, honestly added, still admit a second completed grid with two rows exchanging a pair of digits in columns whose sums happen to match, so the buyer who finds it has followed every printed rule and arrived somewhere your key calls wrong. The buyer does not judge your book by the puzzle on the listing. They judge it on the quiet Sunday evening when puzzle forty-one's seventh column will not close and one stubborn total insists the digits above it must add to a number no legal digits can make.
That is why the unit of quality in this genre is not the puzzle, it is the verified book. Every printed sum in the file has to carry the same five promises at the same standard: rows satisfied as permutations, every column re-added to its printed foot β recomputed, not remembered β touching cells different everywhere including the diagonals buyers forget, givens exactly as designed with every 0 intact, and one solution only. A book that keeps those promises on ninety-nine puzzles and breaks one has not scored ninety-nine percent. It has taught the buyer that your foot row cannot be trusted, and every later stall β including the fair stalls you designed on purpose, where a column could still be one of two digit sets and the buyer must earn the difference from the touching rule elsewhere β will be read as another misprint.
Sell the book as that promise, plainly. State the width is ten and the digits are 0 to 9, and say in plain words what a row is: each row, when finished, holds every digit once, in some order. Say what the number under a column is: the digits in that column, added together, exactly β and work one column aloud in the introduction, slowly: here is a solved column, here are its digits read top to bottom, here is the addition, here is the printed number it matches. Then work the touching rule on the same solved example, because it is the rule buyers under-read: point at one digit, point at the eight cells around it, and show that none of them holds it β including the two diagonal neighbours a Sudoku-trained eye will not check. State how many rows your edition's grids have and keep that count fixed through the book, state that a blank cell is an empty cell to fill while a printed 0 is a digit already placed, and state how difficulty is graded. A buyer who can re-add one solved column and re-check one digit's neighbourhood before page one will not write the review that says the numbers lie. A buyer who discovers on page thirty that columns were allowed to repeat, or that diagonal neighbours counted, has been ambushed by a convention you owed them on page one.
The contract, part by part
The row rule is the genre's spine: in the finished grid, every row holds 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, each exactly once. That single sentence fixes the width at ten forever β a Tenner Grid cannot be eight wide or twelve wide, because a row is the full set of ten digits β and it fixes every row's own total at 45, which becomes an audit tool below. It also means every digit appears in the finished book exactly as many times as the grid has rows: in a three-row edition, exactly three 0s, three 1s, and so on, one per row, a counting fact your introduction may teach and your audit must use.
The column rule is the row rule's deliberate opposite. Down a column, digits may repeat β the contract forbids a repeat only where the touching rule forbids it, between neighbouring rows β and what binds the column instead is arithmetic: the digits in it add to the printed number beneath it. That number binds only its own column. It says nothing direct about any other column, however close their totals sit, and nothing at all about any row beyond what the shared cells carry. The range of a column sum depends on the edition's row count, and the book must be honest about that arithmetic: in a three-row grid a column holds three digits, so its sum runs from small β 0+1+2 is 3, the least a touching-legal column of three distinct neighbours can total if its top digit is 0 β up to 9+8+7, which is 24; a printed sum outside the range your row count allows is not a hard puzzle, it is a misprint, full stop. And the ten column sums of one puzzle are not independent decorations: added together, they must total 45 times the number of rows, because every row contributes 45. A foot row that fails that grand total was wrong before any solving began.
The touching rule deserves the slowest statement of all, because every word in it excludes a real misreading. Touching means all eight surrounding cells: left and right in the row β already guaranteed different by the row rule, but stated so the rule reads complete β above and below in the column, and the four diagonals. The diagonals are the genre's signature and its most-dropped clause: a digit placed in one row forbids the same digit in the three cells of the next row that sit under it and to either side of it, so when a digit repeats from one row to the next, it must jump at least two columns sideways. Two rows apart, no touching is possible vertically, so a digit may return to the same column β and a column in a taller edition may therefore hold the same digit twice, legally, with exactly one row's distance between the copies. A book that prints the rule as "adjacent cells differ" without naming the diagonals has under-stated its own contract, and a generator that checks only the four straight neighbours will produce puzzles that are false under the rules the listing promised.
Given integrity is the part setters most often break in production rather than in design. The givens printed in the grid are one fixed problem statement, and changing any of them after the uniqueness check invalidates the check. In this genre the fragile given is 0. A 0 is a real placed digit β it completes a row's set, it contributes nothing to its column sum, and it forbids 0 in all eight neighbours. Production pipelines break it in both directions: a typesetting default that treats 0 as empty and blanks it, deleting a given; and a solver's pencilled 0 in a working file promoted into print as a given that design never ordered. Either error leaves a book whose puzzles may still be beautiful and are no longer verified. Uniqueness closes the contract: exactly one completed grid may satisfy every row, every printed column sum and the touching rule together, tested against the printed statement β the givens and sums in the shipped file, not the design file.
Variants must be flagged wherever they appear, never smuggled. The edition's row count is itself a form choice: a three-row book and a four-row book are different contracts in everything but name β different column-sum ranges, different repeat geometry down a column, different solving feel β and mixing heights inside one book without labelling the change at the chapter head breaks the buyer's learned arithmetic exactly where they trust it most. Givens-free puzzles, where the foot row alone must force the grid, are a legitimate expert form and a different promise about solving, and they must be sold as such, not discovered. And any edition that drops the diagonal clause β a straight-neighbours-only relative β is not Tenner Grid under a friendlier setting; it is another puzzle, and the cover, the listing and the page must say which contract each puzzle was actually generated under.
The verification audit: eight checks before any file ships
First, re-add every printed column sum from the key, by hand or by an independent script that did not generate the puzzle: read that column of the completed grid top to bottom, add its digits aloud, and compare with the printed number beneath it. Not the setter's stored sum β the printed one, taken from the final file, because the failures that matter live between the key and the page.
Second, check the grand total of each puzzle's foot row as a separate pass: the ten printed sums, added together, must equal 45 times the edition's row count. This check catches a different family of errors from the per-column pass β a sum row belonging to another puzzle, a totals line computed on a grid with a row missing β because it accounts for every digit in the grid exactly once, and any mismatch proves the foot row and the key parted company somewhere, even before you learn where.
Third, recount every row of the key as a set: each row must hold 0 to 9 exactly once β ten cells, ten distinct digits, none missing, none doubled. It sounds too basic to state in an audit, and it is exactly where a key corrupted by a late edit announces itself: a column sum can still be honestly computed from a grid whose row repeats a digit and omits another, and only the set recount notices.
Fourth, sweep the touching rule across the whole key, cell by cell, diagonals included, as its own pass and never as a by-product of the others. For every cell, compare its digit against all eight neighbours; record any equal touching pair. This is the pass automated spot-checks skip, because a grid can pass every row and sum test while two equal digits sit diagonally adjacent β legal under Sudoku instincts, false under this contract, and visible to any buyer who checks the one neighbourhood your audit waved through.
Fifth, sweep the extreme columns separately. Every printed sum within a few points of your edition's minimum or maximum must have its digit set enumerated and matched against the key: a near-minimum column in a three-row grid is forced toward {0, 1, 2} and its permutations, a near-maximum toward {7, 8, 9}, and those forced sets are the clues buyers use first β and the ones a one-digit misprint most completely falsifies. A sum that is arithmetically impossible for your row count, or possible only with a touching violation, fails here even if it somehow survived the first pass.
Sixth, audit the givens against the design record, 0s first. List every pre-printed digit in the final file and confirm each was ordered β no blanked 0, no promoted pencil mark, no given drifted one cell in layout. Then confirm the opposite error nowhere: no cell the design left empty carries a printed digit in the shipped file. In this genre the given list is short enough to check completely, which means there is no honest excuse for checking it approximately.
Seventh, re-solve each puzzle from its printed statement alone β printed givens, printed sums, touching rule as printed β and confirm exactly one completion exists and that it is reachable by deduction, with the intended difficulty's techniques, without guessing. During this pass, note whether removing any single given still leaves the solution unique; a book may include a redundant given knowingly, for teaching or rhythm, but it may not discover its redundancy from a buyer. The statement tested must be the statement shipped, in the shipped file, not the design file.
Eighth, read the sums off the printed proof, as a buyer, in reading order, and check alignment physically: each sum sits centred under its own column, none has drifted into the gutter between two columns, no two-digit sum has lost a digit to the trim, and the sum you read first is the sum the audit added first. Then open the key section and confirm the key prints the same foot row in the same order under its solved grids β a key without its sums is a key that cannot be checked, and a buyer who cannot check a column will assume the column is wrong. A book that passes all eight checks, puzzle by puzzle, has earned the sentence its listing wants to say.
Difficulty is how the sums bite, not how many givens you removed
New sellers grade Tenner Grid by given count, because placement puzzles taught them to. Given count is a real lever here, but it is not the first one, and the honest levers are these. Column-sum extremity comes first: a very low total forces its column toward the smallest digits and a very high one toward the largest, and a foot row rich in extremes hands the buyer forced sets all across the grid, while a foot row of middling totals β every column compatible with many digit sets β can make a generously given puzzle far harder than a sparser one holding two extremes. Given placement comes second: a given does double work in this genre, fixing its own cell and, through the touching rule, striking its digit from eight neighbouring cells and from its whole row β so where givens sit, and how their forbidden zones overlap, matters more than how many there are. Adjacency pressure comes third: count how often a digit's repeat in the next row is squeezed by the two-column jump the touching rule demands β puzzles whose rows must keep re-placing the same large digits under that squeeze solve harder than their sums suggest. Decision distance comes last and matters most for the hard grades: count the steps from the printed statement to the first forced placement that is not an extreme column read at sight β a long walk through set arithmetic and touching eliminations is difficulty a buyer can feel, and it is designed, not accidental.
The grid's width is no lever at all: it is ten in every Tenner Grid ever printed, fixed by the digit set itself. The edition's row count is the weakest lever: adding a row adds information β one more digit in every column sum β at the same time as it adds cells to place, so taller is not reliably harder, and a book that grades by quietly changing heights is grading by changing the contract. That fixity is a selling point if you use it honestly β the buyer who learns your grading learns it once, and an Easy in chapter one means the same arithmetic as an Easy in chapter nine β and it is why difficulty claims must be made in the variant's own terms. An honest grade states, per section, how many givens the puzzles carry, what share of column sums are extreme, and whether the hardest step is set arithmetic, a touching squeeze or a long decision walk. Never grade by removing givens silently and calling the result Expert: a puzzle starved of givens whose sums sit in the comfortable middle will feel to the buyer not hard but empty β the information itself has left the page, and what remains is guessing wearing a difficulty label. Grade instead by moving sums toward the middle, spacing givens so their forbidden zones barely overlap, and lengthening the decision walk, and say that is what you did.
Print honesty: a sum under the wrong column is a sum you never gave
The foot row is this genre's page, and it is the first thing careless printing destroys. The ten sums live below the grid, closer to the paper's bottom edge than any given digit, exactly where domestic printers clip, where print-on-demand trim variance wanders, and where a fit-to-page rescale shrinks small numbers fastest. So the file must be built with the foot row inside a generous safe area, proven on a printed proof and not on screen: if a 17 can lose its second digit to a trim, the puzzle has not been made harder, it has been falsified. Alignment is the second print duty. Each sum must sit unambiguously centred under its own column, at a consistent distance from the grid, because a total floating between two columns will be read for both and believed for neither β and a foot row that has slipped half a column in export is the single most destructive layout error this genre owns, since it falsifies all ten clues at once while looking perfect. Two-digit sums need tabular alignment so that 14 and 11 cannot be confused at a glance and so the eye can run along the row comparing values. The 0 digit carries a print duty of its own: givens must be set in a face and weight where a printed 0 cannot be mistaken for an empty cell's faint placeholder, and blank cells must be truly blank β no ghost digits, no watermark numbers, nothing a buyer could read as a given that design never placed.
The worked example carries print duties of its own. It must be printed at the same size as the puzzles, with its full foot row in place, and talked through completely β one column added aloud, one row read as a set, one digit's whole neighbourhood checked aloud, diagonals included β so the buyer's first encounter with your sums is a success they can repeat. The key section must resist the usual key-section economies: do not drop the foot row from the solved grids to save space, do not print the key at a size where two-digit sums blur, and do not mirror or rotate the key grids without moving their sums with them. A mirrored solution with an unmirrored foot row is a new, unsolved and usually false puzzle wearing a key's authority. State the printing facts on the listing and in the book: the page size the file is built for, that the foot row must not be cropped, that fit-to-page printing is safe only because you left the safe area β and then make sure the last claim is true on the proof in your hand.
Licensing, provenance, and whose variant this is
Tenner Grid belongs to the shared culture of digit-placement puzzles: it circulates in the German puzzle tradition as Zehnergitter, appears in puzzle collections and solver sites under both names, and its rules β the ten digits, the column sums, the touching clause β are common property that no seller can honestly claim or license as their own invention. That freedom has exact limits. It covers the rules. It does not cover other people's puzzles. A named setter's or a puzzle site's Tenner Grids β the ones printed in books, posted on collection sites or sold in magazines β are their makers' work, in their selection, their givens, their sum patterns and their grading, and copying grids because the rules are shared is the same error as copying a Sudoku book because Sudoku is old. Generate your own, or license specific puzzles from the setter who made them, in writing, for download sale.
Provenance honesty also runs in the other direction, toward the buyer. If your book's puzzles are computer-generated, say so, and say what verified them β the eight checks above are a claim you can make precisely. If a human setter tuned them, name the setter as your other books would. What a listing may not do is borrow authority it does not hold: competition branding for puzzles that never stood in a competition, a famous setter's name in the keywords for a book they had no part in, or the word official for a form nobody officiates. Form honesty needs the same candour at the book level: if a chapter changes the row count, drops the diagonal clause or removes the givens, the chapter head names the change, because the buyer's consent to a different contract is only real if it is informed before the purchase, not discovered at the first impossible sum. And keep the form's name clean in your own catalogue: tenner means rows of 0 to 9, one sum under every column, touching cells different; a book of ordinary Sudoku with a sums worksheet at the back is not a Tenner Grid book, and selling it as one buys a week of clicks with a season of returns.
Finally, the errata rule, which is where a download format should beat print and usually does not. When β not if β a sum error is found after release, the corrected file goes to every past buyer, not just to future ones: the same product, fixed, re-delivered through the storefront the buyer bought it on, with a note naming the puzzle and the sum that changed. That re-delivery is the whole reason to sell puzzle books through a delivery tool like FileFreight instead of a bare file link β the buyer list and the corrected file have to be able to find each other months later, on the day a reader writes in to say puzzle forty-one's seventh column cannot be made to add up. Print cannot do that. A download seller who will not do it has chosen print's failure mode at a download's price, and the review that follows will say so, accurately.
The launch checklist
One, state the contract on the listing and on page one, in the same words: every row holds 0 to 9 exactly once, the number printed under each column is the sum of that column's digits, touching cells β horizontally, vertically and diagonally β always hold different digits, and a printed 0 is a placed digit, never a blank. Two, work one example completely β one column added top to bottom, one row read as a full set of ten, one digit's eight neighbours checked aloud β at full puzzle size, with its foot row printed exactly as the puzzles print theirs. Three, run the eight-step audit on the final file, not the design file: column re-additions, foot-row grand total, row set recounts, the full touching sweep with diagonals, extreme-column enumeration, the given-by-given audit with 0s first, a unique re-solve from the printed statement, and a buyer's read of the printed proof including the key's own foot rows. Four, grade honestly in the variant's terms β sum extremity, given placement and overlap, adjacency pressure, decision distance β keep the edition's row count and the width's promise identical in every section, and label any height change, givens-free chapter or relaxed-touching chapter at its head with its own contract. Five, prove the print: foot row inside the safe area on a physical proof, each sum centred under its own column, two-digit sums legible and aligned at arm's length, printed 0s unmistakably distinct from blank cells, margins uncropped at the stated page size. Six, keep provenance clean: rules shared, puzzles your own or licensed in writing, generation and verification stated as they are, no borrowed names, no competition claims the puzzles have not earned. Seven, wire the errata rule before the first sale: a corrected file can be re-delivered to every past buyer through your storefront, the product description promises that it will be, and the first correction β when it comes β is sent with the puzzle and the changed sum named in the note.
A Tenner Grid book is a small thing to promise and a strict thing to keep: ten digits in every row, ten numbers standing under the grid claiming to be sums, and one quiet rule about touching cells that reaches into every neighbourhood on the page. The buyer cannot see your generator, your setter notes or your intentions. They can only add a column, check a neighbourhood, and decide whether the number at the foot told the truth. Sell books where it always did.
