Block Puzzle

Three shapes sit under the board. Drag one onto the grid, or tap it and then tap where you want it; the preview shows exactly which cells it will take before you let go. A shape needs every one of its cells to land on an empty square inside the grid — it is never rotated, never flipped and never split up. The instant it lands, every row and every column that is now completely full clears, all of them together. A slot stays empty until all three have been used, and only then are three more dealt.

Nothing else ever moves. There is no gravity, nothing falls from the top, and no timer is counting down anywhere — the board changes only when you change it, which is why this is a puzzle you can leave half-finished and come back to. Your board is saved on your own device, and the page works with the network unplugged.

One point for every cell you place, so the nine-cell square pays nine and a single block pays one. Clearing lines is where the game actually lives, and clearing several at once is worth far more than clearing them one at a time: n lines in one placement pay 5n(n+1), which is ten points times the nth triangular number.

Six is the ceiling, and it is a real one rather than an arbitrary cap. A line only ever clears the moment it fills, so no line is ever sitting full when you place — which means every line you clear has to contain one of the cells you just put down, and no shape in the bag reaches more than six lines at once. A five-long line spans five columns and one row; the nine-cell square spans three rows and three columns. Emptying the grid outright pays a further 100, which makes 319 points the largest move available on this board: the big square, dropped into a gap where it completes three rows and three columns and leaves nothing behind.

When none of the shapes still on offer fits anywhere — and not one move before that. This is the rule implementations get wrong, usually by checking only the first shape, or by giving up as soon as the board looks crowded. Here the test is exhaustive: every remaining shape is tried in every one of its legal positions on the board as it stands, after clears, and the game ends only if all of those come back empty.

The distinction matters more than it sounds. Across 200 boards played out by the built-in hint, 170 died with exactly one shape left on the tray, 25 with two and 5 on a freshly dealt three. A game that gave up when the first of three did not fit would have ended most of those boards several moves early, and the score you finished with would have been somebody else's.

Twenty-seven of them, drawn one at a time and with equal probability. Because nothing rotates, every orientation is its own shape in the bag — corners come four ways at three cells and four more at five, tees come four ways, diagonals lean both ways, and each straight line exists both across and down.

That is 104 cells across the bag, an average of 3.85 per shape, and 1,971 legal opening placements on an empty grid. The nine-cell square is the piece that ends games: it turns up in roughly one tray in nine (10.8% measured over 60,000 trays), and it has 64 homes on an empty board but a median of only 4 by the time half the grid is filled.

Every board has a number, and that number is the whole game. The sequence of trays is a pure function of it, so board #482137 offers exactly the same shapes in exactly the same order on any device, today or in five years, with no server involved. That is what makes Replay this board on the end screen honest — it is the identical run, not a fresh one — and it is how the daily board works without an account.

Par is 600 points. It is set from the game rather than picked out of the air: the hint button's own player, taking its own advice on every move, plays boards 1 to 200 to a mean of 727 and a median of 571.5 — the middle pair score 569 and 574 — and reaches 600 on 92 of them. Beat par and you have genuinely out-played the hint.