🔧 Step-by-Step Answer Walkthrough For Easy Level
The teal equals block in the bottom-left corner covers four cells and every one of them must hold the same pip. Only the 4/4 double has two identical halves, so it is the tile that has to sit inside the block. It stands vertically down the block's left column, 4 in the top-left cell and 4 in the bottom-left cell, which settles the block's value as 4. Both tiles crossing into the block now have to contribute a 4 as well.
The block's top-right cell is reached from the pink equals pair above it, and the tile that can hand the block a 4 there while also filling a pink cell is the 5/4. It stands vertically with 4 in the block's top-right cell and 5 in the pink pair's left cell, which immediately fixes the pink pair's value at 5.
Ask where a 6 could possibly live. The purple sum-5 pair cannot hold it, the pink equals pair is already spoken for at 5, and the teal block runs on 4s, so the only home left is the orange greater-1 cell along the bottom. The 6/4 tile lies horizontally across that edge, 6 on the right in the orange cell and 4 on the left in the block's bottom-right cell, completing the teal block.
The purple sum-5 pair in the top-right needs two pips adding to 5, and its left cell belongs to the 3/5 tile while its right cell belongs to the 2/1 tile. If the 3/5 tile pushed its 5 into the purple pair, the other cell would need to be 0, and no remaining tile can supply that. So 3 rises into the purple pair's left cell and 5 drops into the pink pair's right cell, giving the pink pair its second 5. The purple pair's remaining cell is therefore 2, the lower half of the 2/1 tile, and the 1 of that tile fills the uncoloured square at the top-right.
🔧 Step-by-Step Answer Walkthrough For Medium Level
The purple less-1 cell in the top-right corner has exactly one neighbour, the right cell of the pink sum-3 pair, so the tile there stands vertically and its pip is a 0. The pink less-1 cell at the bottom-right takes the other zero and lies horizontally with the uncoloured square to its left, which fixes the 0/3 tile as 0 on the right and 3 on the left in the free square.
The blue greater-9 pair in the centre and the green greater-9 pair on the right each need two pips that beat 9 together, so both cells in each pair are heavy. The 5/5 double lies horizontally along the middle row, its left half filling the blue pair's right cell and its right half filling the green pair's left cell, giving 10 on both sides.
The 5/4 tile stands vertically at the far right, 5 falling into the green pair's right cell and 4 rising into the teal greater-2 cell, which satisfies the greater-2 constraint. Meanwhile the blue pair still needs a 5 on its left, and the 1/5 tile provides it: it lies horizontally with 5 on the right in the blue pair's left cell and 1 on the left in the upper cell of the orange sum-1 pair.
The orange sum-1 vertical pair is now half solved with a 1 on top, so the lower cell must be 0. The 4/0 tile lies horizontally along the bottom-left, 0 on the left in the orange pair's lower cell and 4 on the right in the purple greater-3 cell, which clears the greater-3 requirement.
The 1/0 tile stands vertically in the top-right, 0 above in the purple less-1 cell and 1 below in the pink sum-3 pair's right cell. The 4/2 tile lies horizontally near the top, 4 on the left in the uncoloured square and 2 on the right in the pink sum-3 pair's left cell, completing the sum of 3. That accounts for every tile: both greater-9 pairs read 5 and 5, the two less-1 cells hold 0, and the orange pair reads 1 over 0.
🔧 Step-by-Step Answer Walkthrough For Hard Level
The green sum-0 cell at the bottom-left corner can only hold a 0. The tray has no 0/2 tile, so a horizontal pairing with the purple sum-2 cell beside it is impossible; the partner has to be a 1 from the uncoloured square directly above, so the 0/1 tile stands vertically there, 0 below in the green cell and 1 above in the free square. One column to the right, the purple sum-2 cell mirrors it: the 1/2 tile stands vertically with 1 in the second uncoloured square and 2 below in the purple cell.
The pink equals column is three stacked cells that must all match. The 0/0 double is the tile that fits inside it, filling the top and middle cells with 0, so the column's value is 0. The remaining cell at the bottom of the column is supplied by the 3/0 tile, which stands vertically with 0 up into the column and 3 down into the top of the orange greater-9 column.
The four-cell blue equals block at the bottom-right repeats a single pip. The 5/5 double stands vertically inside it, giving the middle-right and bottom-right cells matching 5s, so the block's value is 5. Its two top cells are fed from above: the 3/5 tile stands vertically over the top-left corner cell, 5 down into the block and 3 up in the uncoloured free square, and the 4/5 tile stands vertically at the bottom of the teal greater-8 column, 4 in that column's lowest cell and 5 down into the block's top-right corner cell.
The orange greater-9 column already has a 3 in its top cell. The 4/3 tile stands vertically beneath it, 4 in the middle cell and 3 in the bottom cell, so the column reads 3, 4, 3 and beats 9. The teal greater-8 column is completed by the 3/2 tile, which stands vertically with 3 in the top cell and 2 in the middle cell, joining the 4 already sitting in the column's lowest cell for a total of 9. That leaves the center-right uncoloured square holding the 3 from the 3/5 tile.
The blue sum-6 cell is a single cell, so it must hold a 6, and the 2/6 tile is the only tile in the tray carrying one. It stands vertically with 6 in the blue sum-6 cell and 2 below in the upper cell of the pink unequal pair, which is exactly why that pair is labelled unequal: its other cell has to differ, and it does.
The 1/5 tile stands vertically on the left, 1 in the orange sum-1 cell and 5 down in the purple sum-5 cell. The 4/1 tile lies horizontally at the left edge, 1 on the left in the teal sum-1 cell and 4 on the right in the lower cell of the pink unequal pair, so that pair reads 2 above and 4 below. The 1/1 double stands vertically in the green sum-2 pair, 1 in each cell. Finally the 2/4 tile lies horizontally across the top-left, 2 on the left in the uncoloured square and 4 on the right in the purple sum-4 cell, and every tile in the tray is placed.
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