A short history of number puzzles in print

Number puzzles are much older than the puzzle page, and the puzzle page is much older than the app. The line runs from arrangements that were treated as objects of contemplation, through a hundred years of newspapers needing something to put next to the crossword, to a format where everyone plays the same puzzle on the same day and stops. Chain sits at the end of that line, and it is closer to a 1980s television round than to anything in a grid.

Magic squares came first

The oldest number puzzles are arrangements, not questions. A magic square is a square grid of distinct numbers whose every row, column and main diagonal add to the same total, and the interesting thing about them is that they were valued long before anyone treated them as a puzzle to be solved under time pressure.

The 3×3 Lo Shu square is the one everybody eventually meets. Its rows, columns and diagonals each sum to 15, and it is the only order-3 magic square there is, up to rotation and reflection — every "different" one you can write down is the same square turned around. Its origin in Chinese tradition is legend rather than dated record, which is worth saying plainly; what is documented is a long written history around it. Yang Hui's treatise of 1275 is the oldest surviving Chinese work to set out magic squares larger than 3×3, covering orders three through ten.

They travelled. A 4×4 pandiagonal square with a magic sum of 34 is inscribed on the wall of the Parshvanath temple at Khajuraho in India, dated to the 12th century. And in 1514 Albrecht Dürer put an order-4 square, also summing to 34, into the engraving Melencolia I, arranging it so the two middle numbers of the bottom row read 15 and 14 — the year he made it.

None of these are puzzles in the modern sense. Nobody handed you a partly filled Lo Shu square and asked for the rest. But they establish the thing every later number puzzle depends on: that a constraint on sums is enough to make an arrangement feel discovered rather than invented.

The crossword invents the puzzle page

The format that made daily puzzling a habit was not a number puzzle at all. Arthur Wynne, a journalist from Liverpool working in New York, published a "word-cross" in the New York World on 21 December 1913. It is generally cited as the first crossword.

The commercial moment came eleven years later. In 1924 Simon & Schuster published the first crossword puzzle book — the suggestion came from co-founder Richard Simon's aunt — with a pencil attached. It was an immediate bestseller and it established that people would pay for puzzles in volume.

Newspapers were slower and, in one famous case, sniffy. The New York Times did not run a crossword until 15 February 1942, when it was framed as relief from war news, with Margaret Petherbridge Farrar as its first puzzle editor; she held the job until 1969.

Two habits date from this period, and both matter for what came later. Puzzles got a fixed place in the paper, which meant a fixed daily supply. And they got an editor, which meant somebody was responsible for difficulty being consistent from one day to the next. Every daily puzzle since has needed both.

Cross sums: arithmetic borrows the crossword's shape

Once the puzzle page existed, it needed filling, and the obvious move was to keep the crossword's grid and swap the letters for digits. The result is the puzzle North America knew as cross sums: a crossword-shaped grid where each run of white cells has a clue giving the sum of its digits, and you fill it with the digits 1 to 9 without repeating one inside a run. Jacob E. Funk, a Canadian working at Dell Magazines, coined the English name in 1966.

The same puzzle became enormously popular in Japan under the name kakuro, where it was for years the leading logic puzzle in print — until 1992, when Sudoku passed it.

The design lesson from cross sums is that arithmetic works fine as puzzle material as long as the arithmetic itself is easy. Adding to 16 is not the challenge; working out which digits can add to 16 given what crosses them is. Every good number puzzle since has kept the sums small.

Number Place becomes Sudoku

The best-documented route from a magazine page to a global habit belongs to Sudoku, and almost every step of it is a person doing something deliberate.

The modern puzzle was designed by Howard Garns, a 74-year-old retired architect from Connersville, Indiana, and first published by Dell Magazines in 1979 in Dell Pencil Puzzles and Word Games under the name Number Place.

It reached Japan through Nikoli, whose president Maki Kaji ran it in Monthly Nikolist in April 1984 as Sūji wa dokushin ni kagiru — "the digits must be single" — later shortened to Sudoku. Nikoli then did the editorial work that made it a puzzle rather than a filling exercise: in 1986 it restricted grids to at most 32 given clues and required the givens to be rotationally symmetric. Those two constraints are why a Nikoli-style Sudoku looks like a designed object.

The global spread came from Wayne Gould, a Hong Kong judge who spent six years from 1997 writing software to generate puzzles quickly. The first newspaper outside Japan to run them was the Conway Daily Sun in New Hampshire in September 2004, and The Times of London launched its Sudoku on 12 November 2004. Within a year the puzzle was in newspapers everywhere.

The numbers round: a puzzle on a clock

The direct ancestor of Chain is not on a page at all. It is a television round.

The French programme Des chiffres et des lettres was created by Armand Jammot. It began in September 1965 as Le Mot Le Plus Long — "the longest word" — with letters rounds only, and the numbers were added when the format returned in January 1972. Its British adaptation, Countdown, premiered on 2 November 1982 as the first programme broadcast on Channel 4.

The numbers round works like this. Twenty-four face-down tiles are available: twenty "small" numbers, two each of 1 to 10, and four "large" ones — 25, 50, 75 and 100. The contestant picks six. A random three-digit target from 100 to 999 is generated. Then thirty seconds, the four basic operations, only exact division, no fractions and no negative numbers along the way. A number cannot be used more times than it appears on the board, and you do not have to use all six.

That is a genuinely well-made puzzle and it is nearly forty years old. The intermediate-value rules — exact division, stay positive — are what stop it becoming a grind, because they cut the search space hard enough that a person can hold it in their head.

What Chain kept and what it changed

Chain is the numbers round rebuilt as something you play once a day, alone, without a clock ticking at you. The bones are the same: a starting value, a target, a small set of operations you may use at most once each, and exact division only.

The changes are all in the direction of a fixed answer. Chain gives you a start between 10 and 99, a target between 100 and 999, and a hand of five tiles — six on hard days — where each tile is a whole move: +n, −n, ×n, ÷n, or swap digits, which reverses the digits of your running value. You must use exactly the number of moves shown, and exactly one subset of the hand reaches the target. On Countdown, "close enough" scores points and there are usually several ways there. In Chain there is one set and you either have it or you do not. The rules cover the details, and the strategy guide covers how to find the set without brute force.

The swap digits tile is the only part with no ancestor in the numbers round. It exists because addition and multiplication alone make the reachable values too predictable, and reversing digits — 173 becomes 371, 120 becomes 21 — is the one cheap operation that changes a number's size without a multiplier.

Everyone gets the same puzzle, and then stops

The last shift is not about the puzzles but about the schedule. Print always had one puzzle a day because a paper comes out once a day. The early web threw that away — puzzle sites offered unlimited generated grids, and unlimited turns out to be worse. Nothing to compare, nothing to finish, no reason to come back tomorrow rather than play forty now.

The daily online format put the constraint back on purpose: one puzzle, the same for everyone, a hard stop when it is done, and a short piece of text you can paste to a friend that shows how it went without spoiling it. That is the newspaper puzzle page rebuilt, minus the paper — and it turns out the scarcity was doing most of the work all along.