Umbra

Where Umbra comes from

Umbra is our take on the light and shadow puzzle, a region-division genre that first appeared under that name in 2014, from the Turkish constructor Serkan Yurekli. It belongs to a quieter branch of the logic-puzzle family than the loops and the number grids: instead of drawing a line or filling in a picture, you carve the board into pieces. Its nearest relative is Fillomino, where regions are kept apart by matching sizes; the light and shadow puzzle keeps them apart by colour instead, which is a smaller rule and a stranger one, because it means the two shades are doing structural work rather than decorative work. An umbra is the fully dark core of a shadow, the part where the light source is hidden completely, and the name suited a puzzle in which the dark is not an absence but a shape with a size and an edge.

There is one property of the genre worth knowing before you start. The clues arrive already coloured, and they have to: the rules constrain which cells share a field, never which colour a field takes, so a board of bare numbers would have two equally correct answers, the one you found and its exact mirror image. Colouring the givens settles it, and every Umbra board has exactly one answer.

From midweek some of those givens arrive as a question mark instead of a number. A ? is a given like any other, one field of one colour, except that its size is not written down and you have to work it out from the fields packed around it. It is the week's second difficulty lever, absent on Monday and Tuesday and most numerous on Sunday, and it changes the character of the solve: instead of filling a size you already know, you are proving what a size must be.

How to get better at Umbra

Start with the ones. A 1 is a field that is finished the moment you place it, and it is worth more than that: every cell it touches must take the other shade, because a same-shade neighbour would grow it to two. One number, five certainties.

Work the edges and corners first. A number in a corner has two directions to grow instead of four, and a number against a wall has three. The board is most constrained where it runs out, so the deductions are cheapest there and they propagate inward.

Count the room a number has. A 5 sitting in a pocket that only has four free cells around it cannot be a 5 there, so something you have already painted is wrong. Running this check the other way is more useful still: when a number has exactly as much room as it needs, its whole field is forced.

Watch for numbers that cannot be neighbours. Two numbers can never end up in the same field, so the cells between two nearby numbers are a battleground. If a cell can only be reached by one of them without joining the other, it belongs to that one.

Use the blank state. Leaving a cell undecided is not indecision, it is bookkeeping. Solvers who paint every cell as soon as they touch it lose the ability to see which parts of the board are still open, and that visible frontier is where the next deduction usually is.

Trust the parity. Because touching fields must alternate, a chain of fields across the board alternates all the way along. Once you have committed to a shade anywhere, the shades of everything connected to it follow. If following a chain brings you back to where you started on the wrong shade, the division you were assuming is impossible.

A round in the life

Thursday, a 7 by 7. You find the two 1s first, already dark on the board, and fence them in, which hands you eight cells of the opposite colour for free. A 6 sits against the left wall with a 4 two cells below it; the corridor between them is three cells wide, and only one of the two can reach the middle cell without swallowing the other's number, so the middle cell is spoken for. The 6 grows down and the 4 is squeezed flat against the wall. In the open middle you have a 5 with exactly five free cells around it, which is not a choice at all. By the time the last blank cell goes down you have not guessed once, and the board reads as a single alternating weave of pale and dark, which is the whole pleasure of the thing: the answer looks less like a solution than like a pattern that was always there.