In 1977 the mathematician Frank Harary asked a noughts-and-crosses question. On an endless sheet of squared paper, two players take turns claiming one square each. The first player is trying to build a particular shape. The second is only trying to stop them. Which shapes can always be built?
He called the shapes animals. One by one they were settled: eleven of them can always be built, and all the others can always be blocked. All except one, a six-square animal nicknamed Snaky. People showed that the usual blocking trick fails against it, that it can be built in three dimensions, and that it can be built if the first player gets one extra square at the start. The plain game on plain paper stayed open for forty-nine years.
On 6 October 2026 OpenAI published a collection of 722 mathematics papers written by one of its internal AI models. One of them, Snaky in 21 Maker moves (dated 25 September 2026), states:
On an empty, infinite grid, the first player can always complete Snaky within 21 of their own moves, whatever the second player does. Rotations and mirror images of the shape count.
The result is OpenAI's model's, not this page's. This page only lets you feel it.
Not with a clever argument you have to take on trust. With a table.
The paper prints 728 numbered cards. Each card is one small promise: if red already owns these squares, and none of the squares in this region has been pencilled out, then red can finish within h more moves. Six cards are obvious (red has five squares of a Snaky and the sixth is free). Every other card is built from earlier ones by a single rule, proved in a page of the paper: red takes one square that sets up several earlier cards at once, arranged so that the only squares all their regions share are squares red already owns. One pencil mark cannot land in all of them, so at least one promise survives.
The last card, number 727, needs red to own nothing at all. Its promise is 21 moves. A hundred-line program in the paper recomputes every card from the printed table.
There is no AI running on this page. Red's entire brain is the paper's table: 722 lines, 38 kilobytes of text, shown below. Red reads its current card and takes that card's square. After your mark, it moves to the first card on the list whose region you have not touched. That is the strategy in section 5 of the paper, followed exactly; nothing searches, nothing learns, nothing adapts to you.
The two things you can switch on are also the paper's own: the net is the current card's region, and the numbers are the promises on the cards your mark would lead to.
Don't take this page's word for it. The button below plays all 379,988 routes again, here, on your device.
the best defence against this table lasts exactly 21 moveswas computed for this page. A different table might win sooner.