Formeto
the sudoku of shapes
Shapes overlap. Every crossing holds a number. Swap two numbers until every shape adds up to the same sum.
the sudoku of shapes
Shapes overlap. Every crossing holds a number. Swap two numbers until every shape adds up to the same sum.
Shapes overlap: a triangle, a square, a circle, sometimes more. On every crossing sits a number.
Tap two numbers and they swap. The goal: every shape must add up to the requested sum — the same for all, or, at higher levels, one target per shape.
No clock rushing you, a hint if you get stuck, and “Undo” if you change your mind. A puzzle is settled in a few well-chosen swaps.
Every day, a new daily puzzle per level: Kid, Warm-up, Stroll, Serious, Expert and Bonus. Solved? “Another one” draws one more, no limit. Finish one level to unlock the next. Free, no account, on a phone or a computer.
Once it’s solved, I tell you how you played: methodical or intuitive, focused or explorer, patient or fast. That’s your Formeto card, and you can keep it.
Like sudoku, everything is already on the board: nothing to invent, nothing to guess, only logic. And like sudoku, each constraint sheds light on another.
But there are no rows or columns here: shapes that overlap, and numbers shared between two figures. You don’t place a digit, you move two. Instead of “every digit once”, the rule is “every shape, the right sum”. It’s shorter than a grid, and it plays with two thumbs.
A number on a crossing counts for every shape that passes through it. Swapping two numbers therefore removes and adds the same value to several sums at once: the whole art is choosing the swap that fixes one shape without breaking another.
The game descends from a mathematical challenge created by Professor Marco Vinicio Vásquez Bernal at the Universidad Nacional de Educación of Ecuador, with the support of the weekly El Heraldo de Azogues (Ecuador) and the company MACOSER S.A., published every week since 2013 and described in an open-access paper: doi.org/10.21017/rimci.1076. Formeto is its playable adaptation: every puzzle is a shuffled solution, so it always has a way out.
Formeto belongs to the family of magic figures, cousins of the magic square, the magic star and Yang Hui’s magic circles (1275) — numbers placed on the vertices or crossings of a figure, with the same sum on every line, every point or every circle. In graph theory, this is a magic labeling (Sedláček, 1963): the crossings are the vertices, each shape is a hyperedge, and a solution gives every hyperedge the same weight.
One invariant rules everything: a number shared by k shapes counts k times, so the sum of the sums equals the sum of the values weighted by the number of shapes they belong to; divided by the number of shapes, it must land on an integer — the “equilibrium value” with which Vásquez Bernal opens his heuristic resolution. And since every move is a transposition, the shortest path to a given solution can be read in the cycles of the permutation: the number of crossings minus the number of cycles. That is what Poto tells you at the end of a game.
If this topic interests you, or if you have suggestions, write to us at contact@portreto.app: between enthusiasts, it is always a pleasure to talk.
Yes, entirely, with no account and no ads. If you want to find your cards again from one game to the next, you can leave your email: it’s optional.
No. The numbers are small and the sums are done in your head. What matters is spotting which pair to swap.
It’s made for it: the board fits the screen, you play with two fingers, nothing to install.
A hint is one tap away, and the Undo button takes you back. The “Five” tutorial puts the idea back in place in three swaps.
It comes from the solution: the game first places the numbers so that everything adds up, notes the sum of each shape (one common target, or one target per shape at higher levels), then shuffles. You can work it out yourself when the target is common: add each number as many times as there are shapes passing through it, then divide by the number of shapes. In “Five”, the numbers 1 to 5 each sit on two shapes: 2 × (1 + 2 + 3 + 4 + 5) = 30, for three shapes, so 10 per shape. And since a swap moves the same value from one crossing to another, this weighted total never changes: the target is fixed before the first move.