Tessera

Start with the regions that force themselves

Each half of a tile shows between zero and six pips, and that limit makes some regions decide themselves. A two-square region with a badge of 12 can only be 6 and 6. A region whose total is 0 must be covered entirely by blank halves. A two-square region marked "=" wants a matching pair — and if a single tile would cover both squares, it has to be a double.

Look for these before placing anything. They fix a tile or two in place, and every fixed tile takes a shape and a pair of numbers out of the tray.

Count the tray

Every tile is used exactly once, so the tray is a constraint just as much as the badges are. If a region needs two 6s and there is only one tile in the tray with a 6 on it, that tile must cover the region with its 6 — and the other 6 has to come from a tile whose far end lies outside. Checking what is left in the tray is often what decides between two placements that both satisfy the badge.

Use the less-than and more-than badges

A badge like "<4" means the numbers covering that region add up to less than 4. On a two-square region that rules out almost every tile half, so the squares want blanks, ones and a two at most. A ">" badge on a small region does the opposite, pulling in the high halves. These are weaker than an exact total but narrow things quickly.

Mind the shapes

Before thinking about numbers, think about coverage. A lone square in a corner, walled in on three sides, can only be covered by a tile running out of its one open side. A long thin corridor of squares can only be tiled one way. Settling the awkward shapes first means the numbers have fewer places to go.

Try things

Placing a tile costs nothing, and a region's badge turns red as soon as it can no longer be satisfied. Use that: lay a tile where you think it goes, watch the badges, and move it if something breaks. When the board is covered, press Check.