Badgers.

Badgers share the sett. Fill the grid so that every row, column and block has each number once. The dotted cages show how many badgers live there in total, and no number repeats inside a cage.

A cage is the group of cells inside one dotted outline, and the small number in its top left corner is what its cells add up to. Cages hold one to five cells and pay no attention to the block lines, so a cage of three can sit in two blocks at once. Nothing is filled in at the start: the cages are the whole puzzle.

Every sett has exactly one arrangement of numbers that fits every row, column, block and cage. When the last cell is right, the game notices by itself.

Picking cells. Tap or click a cell to pick it. Drag across the sett with the mouse or a finger and every cell you run over joins the selection. Ctrl (Cmd on a Mac) plus a click adds one cell or takes it away. From the keyboard the arrows or WASD move the selection and wrap round the edge, so down on the last row comes out at the top; Ctrl plus an arrow widens it, Escape lets it all go. The row, the column and the block are shaded only while a single cell is picked.

Writing. 1 to 9 from the keyboard or the numeric keypad, or the pad under the sett; a six by six takes 1 to 6. With several cells picked, the number goes into all of them, and the same number again takes it back. Delete or Backspace works in one order: the big numbers first, then the marks, then the colour.

Four modes, as four buttons under the pad. Normal writes the big number (Z). Corner puts small numbers in the corners of the cell (X), Centre puts them in the middle (C), and with several cells picked a mark goes on everywhere or, if they all have it, comes off everywhere. Colour paints the cell in one of nine colours (V). Space walks round all four; holding Shift means Corner and holding Ctrl means Centre for as long as the key is down. A big number covers the marks of its cell without throwing them away, so Delete brings them back.

Undo and Redo are unlimited: U or Ctrl+Z back, R, Ctrl+Y or Ctrl+Shift+Z forward. Ctrl+R is left alone; it reloads the page. Restart takes the numbers, the marks and the colours off; the clock keeps running and one Undo brings everything back. P pauses.

Check first tells you only how many numbers are wrong and which rows, columns or blocks they sit in; press it again and it marks them. With cells picked, only their rows, columns and blocks are checked. Hint names the rule and the place without giving the number away, and the second press writes that one number and explains it. If something on the board is already wrong, the hint points there first. Hints and checks are free and counted, and shown when you finish. Nothing lights up while you play: finding a mistake is part of the puzzle.

The clock runs from your first number to the last cell and pauses when you leave the tab or sit still for a minute, which also hides the sett. Your progress, time, history and day streak stay in this browser, and in your account when you are signed in, so you can continue on another device. The day turns over at midnight, Bratislava time, wherever you are. Only the sett of the day counts towards the streak, the archive is for practice; once you are five days in, a single missed day is forgiven, at most twice a month.

Monday and Tuesday are easy: six by six, numbers 1 to 6, blocks of two rows by three columns. From Wednesday on the sett is nine by nine with numbers 1 to 9 and blocks of three by three, medium on Wednesday and Thursday, hard on Friday and Saturday, and the challenge on Sunday. The week strip under the sett takes you to the other days; the archive goes back a year, and the practice sets have eight setts of each level with no date attached.

Difficulty is measured, not guessed. Every sett is solved by a program that only knows named rules, in three layers: the plain ones (a cage of one cell, a total that can be made in only one way, the single number a cell has left, and a number with only one place left in its row, column or block), the patterns across a whole line or cage (every row, column and block adds up to the same total, so cages lying inside one leave a cell over and cages reaching into one stick a cell out; a pair of cells holding two numbers between them; a total narrowed by what the crossing lines allow; a cage that lies inside one line keeping its numbers for itself), and the hard one (writing a number in and dropping it because it runs into a contradiction). Easy and Medium never need that third layer; Sunday leans on it the most.

Short cages with extreme totals are the way in. Two cells adding to 3 can only be 1 and 2; to 4, only 1 and 3; to 16, only 7 and 9; to 17, only 8 and 9. Three cells adding to 6 are 1, 2 and 3; to 24, they are 7, 8 and 9.

Every row, every column and every block adds up to 45 on a nine by nine, and to 21 on a six by six. Add up the cages that lie wholly inside one block: whatever is missing belongs to the cells the cages left over, and a cage that pokes one cell out of the block tells you what that one cell holds.

A cage that lies inside a single row, column or block keeps its numbers to itself, so nothing else in that line can hold them, even before you know which cell of the cage takes which.

When a cage has one empty cell left, its number is simply the total minus what is already there. That one number then narrows the line crossing it, which is how a sett unravels.