🔧 Step-by-Step Answer Walkthrough For Easy Level
The easy tray stops at 5 — there is no 6 anywhere in it — so the two 'greater 4' cells, the teal one near the top-right and the purple one at the bottom-right, can only be 5s. Those are the tray's only two 5s, and they live on the 5/0 and 2/5 tiles.
The purple 'less 2' cell at the top-right corner has exactly one neighbour, the teal 'greater 4' cell directly below it. They must be a single vertical domino, and the only tile that puts a 5 down and something below 2 up is the 5/0. So 0 goes in the purple cell, 5 in the teal cell.
The other 5 has to sit in the purple 'greater 4' cell at the bottom-right, whose only neighbour is the blue equals cell to its left. That is the 2/5 tile lying flat: 2 in the lower blue cell, 5 in the purple cell. The equals pair now needs a 2 above it — and the pink 'less 2' cell just above that has only one free neighbour left, so the 0/2 tile stands vertically: 0 in the pink cell, 2 in the upper blue cell. Blue reads 2 and 2.
The orange 'less 2' cell's only free neighbour is the top cell of the green equals pair, and the tile that fits puts a 0 above a 3 — the 3/0 standing vertically. The green's lower cell then takes the second 3 from the 4/3 tile, which lies flat along the bottom row: 3 on the left in the green region, 4 on the right in the uncoloured square. Every cell is covered.
🔧 Step-by-Step Answer Walkthrough For Medium Level
The green sum-1 cell on the left edge must hold 1, and the tray contains exactly one 1, on the 1/2 tile. Its partner 2 cannot go up into the purple equals block, because the block would then need three 2s and the tray only holds two — so the tile lies flat: 1 in the green cell, 2 in the uncoloured square to its right.
The purple block's three cells must match, so its value has to appear three times in the tray; only 4 and 6 manage that. Take the 6s and the colours jam — the 2/6 tile would drop a 2 into the pink less-7 pair and the 4/4 double eventually has nowhere to go but across the teal unequal pair. So the block is 4s: the 4/4 double lies flat across its bottom row and the 4/5 tile lies flat across the top-left, 4 in the block's top cell, 5 in the left cell of the pink pair.
The pink pair must total under 7 and already holds a 5, so its other cell is 0 or 1; the only 1 is already sitting in the green cell, so it is 0. That cell's only neighbour is the top of the orange column, so the 0/5 tile stands vertically: 0 up in the pink pair, 5 down at the top of the orange less-12 column.
The column's bottom cell touches only the middle cell, so those two are one domino, and with a 5 already in the column the total must stay under 12. The 3/3 double fits at 11; nothing else left in the tray does. So 3 goes upper in the middle cell and 3 lower in the bottom cell.
Two tiles remain: 2/6 and 6/6. The blue 'greater 8' pair on the right needs a total above 8, and 2/6 would give exactly 8, so the pair takes the 6/6 standing vertically, 6 and 6. The teal unequal pair in the centre takes the 2/6 standing vertically — 6 in the upper cell, 2 in the lower, a legal unequal pair. Solved.
🔧 Step-by-Step Answer Walkthrough For Hard Level
Start at the very top-left corner. The uncoloured free square there has only one neighbour, the teal 'less 1' cell directly below it, so those two squares are one domino. The tray holds a single tile with a pip that can sit in a cell wanting less than 1, and that tile is the 2/0: 2 up in the free square, 0 down in the teal cell.
The blue 'greater 5' cell on the left edge, third row down, needs a 6, and the tray carries only two 6s, so this is a big commitment. Its neighbours are the green 'greater 1' cell to the right and the pink 'greater 3' cell below; the tiles carrying a 6 pair it with a 3 or a 1, and neither belongs in a cell that must beat 3. So the tile lies flat: 6 left in the blue cell, 3 right in the green cell.
The pink sum-4 cell in the top-right corner must read 4, and its only neighbours are two cells of the four-cell purple equals block. That block cannot be all 4s: if the corner's 4 arrived with another 4 on the 4/4 double, the block's other three cells would each need a 4-partner and there is no second double to bridge them. So the 4 arrives on the 3/4 tile, standing vertically with 3 below it, and the block's value is 3: the 3/3 double lies flat across the block's top row, and the 5/3 tile stands vertically with 3 up inside the block and 5 down into the top of the purple three-cell block on the right.
The three-cell purple block on the right already has a 5 in its top-left cell from the 5/3 tile, so all three cells are 5s. The 5/5 double stands vertically in its upper-right and lower-right cells, filling the block and completing the second equals region.
The pink 'greater 3' cell pairs with the teal 'less 2' cell directly below it — only the 1/4 tile can put a big pip up and a tiny one down, so it stands vertically: 4 upper, 1 lower. Lower still, the green sum-3 cell must pair with the uncoloured square below it, and since the 0/3 tile is the only way to make the orange sum-3 pair near the top (the block's cells each have just one other free neighbour), the green cell takes the 3 from the 3/2 tile: 3 upper, 2 lower. On the bottom row, the pink sum-4 cell pairs with the orange sum-9 block's bottom-left cell — the 4/2 tile lies flat, 4 left, 2 right — while the teal sum-2 cell takes the 2 end of the 2/5 tile, standing vertically with 5 up in the block's middle-right cell. The 1/1 double stands vertically in the block's left column (1 upper, 1 lower), so the block reads 1, 1, 5, 2. That leaves the 1/6 tile lying flat in the blue sum-7 pair (1 left, 6 right) and the 4/4 double standing vertically in the bottom-right purple pair, 4 upper, 4 lower.
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