🔧 Step-by-Step Answer Walkthrough For Easy Level
Three of the clues touch only one other cell. The orange sum-4 square sits alone in the top-left corner, with the uncoloured square below it as its only escape; the blue greater-2 square on the right edge has just the pink cell beside it; and the bottom corner of the purple block hangs off the cell above it. So the tiles are decided in shape before any pip is chosen — upright at the orange corner, flat at the blue cell, upright at the foot of the purple block.
Because the blue square's only neighbour belongs to the pink pair, the tile serving the blue square also eats one half of that pair. That forces the pink pair to be filled by two different tiles, and it means the lower pink cell has to reach left into the teal column. From here the tile crossing into the teal equals region is doing double duty: one half sits in pink, the other is one of the two matching teal pips.
The teal pair needs identical pips, and the only tile that fits the crossing is the 2/4: it lies flat with 2 in the upper teal cell and 4 in the lower pink cell. Pink now needs 8 across two cells, so the upper pink cell must also take 4 — which is the 4/3 laying flat through it, sending its 3 into the blue greater-2 square to satisfy that clue at the same time.
The lower teal cell still needs a matching 2, and the tile that supplies it is the 2/0 lying flat: 2 in the teal column so the equals holds, and 0 passed into the top-left cell of the purple block. Purple therefore needs 8 from its last two cells — the 2/6 standing upright at the right end, 2 up and 6 down. The final tile, the 4/1, stands in the top-left corner with 4 in the orange sum-4 square and 1 dropping into the uncoloured free square.
🔧 Step-by-Step Answer Walkthrough For Medium Level
The blue sum-0 square on the top edge can only hold one pip value, and the tray has exactly one tile carrying it: the 0/4. Its sole neighbour is the left cell of the green unequal run, so the tile stands vertically — 0 up in the sum-0 square, 4 down in the first of the three unequal cells.
The orange greater-4 square rules out almost everything: there is no 5 anywhere in this tray, and the only 6 lives on the 6/3. So that square takes 6, and its partner falls straight down into the middle cell of the pink less-8 run — a 3 that keeps the run comfortably under its limit.
The purple equals block in the top-left needs three identical pips, and the 4/4 double is the natural spine: it lies flat across the top pair. The third cell, the one directly beneath the left end, then has to match — the 4/1 stands upright there, putting 4 in the triplet and 1 down at the left end of the pink run. The run now reads 1 and 3 with one cell left.
Two more lone squares sit on the right. The purple sum-2 square takes exactly 2, and the pink sum-3 square takes exactly 3. Each pairs upward into the green unequal run: the 2/2 double stands upright with 2 down in the sum-2 square and 2 up in the middle of the run, while the 3/3 double stands upright sideways-on with 3 up in the run's right cell and 3 down in the sum-3 square. Green now reads 4, 2, 3 — three different pips.
One tile is left. The 3/2 stands vertically at the right end of the pink less-8 run: 3 in the run and 2 down in the teal less-3 square, which is well below its limit. The pink run finishes as 1, 3, 3, and every region on the board is satisfied — the unequal trio, the equals triplet, the two zero-and-greater singletons, and the small sum squares on the right.
🔧 Step-by-Step Answer Walkthrough For Hard Level
Start at the orange greater-5 square in the bottom-left corner. It is a single cell, its only neighbour is the cell above, and it must exceed 5 — so it takes the maximum pip and its tile stands vertically. Now read the green sum-5 square to the right: it has just one neighbour, the right-hand cell of the blue sum-5 pair, so a flat tile spans them and the green square takes 5 while the blue pair's upper cell takes 4. That forces the pair's lower cell to 1 — and since the vertical tile beneath it carries the maximum, it can only be the 6/1: 1 up, 6 down in the orange corner. The flat tile is the 4/5.
The purple sum-0 square near the bottom has one neighbour, the top-left cell of the teal sum-5 block below it. Two matching zeros are needed, and the tray holds a single double zero: the 0/0 stands upright, 0 up in the purple square and 0 down on the corner of the four-cell teal block. That block now needs five more from three cells.
The purple sum-18 run across the top-left is three cells with the highest target the board permits, so each of its cells must be maxed out. The 6/6 double lies flat over the left two, and the right-hand cell can only be fed from below — the 4/6 stands vertically, 6 up in the run and 4 down in the top-right cell of the orange sum-12 block. That block now needs 8 from its remaining two cells, which the 4/4 double supplies lying flat.
The blue sum-6 block on the right settles into 2, 2, 2 — the 2/2 double flat across its bottom two cells, and a vertical tile above carrying 2 down from the top edge. That upper tile also serves the pink sum-5 square in the top row, so it is the 5/2: 5 up in the pink square, 2 down at the block's top-left. The teal less-4 pair on the top-right is then free to take the 2/1 lying flat, 2 on the left and 1 on the right.
The teal sum-0 square in the middle of the board has only two neighbours, and the one above it is the pink greater-3 square. The 4/0 stands upright there, 4 up to satisfy the greater-than and 0 down in the teal square. That leaves the orange unequal pair on the right free for the 6/2 lying flat: 6 on the left, 2 on the right, two happily different pips.
The green sum-0 square on the left needs a zero, and its one open neighbour is the uncoloured square above, so the 0/3 stands upright with 3 up and 0 down. Directly beneath it, the purple sum-9 pair takes the 3/6 upright — 3 up, 6 down. Finally the pink equals column in the bottom-right corner: the 1/1 stands over its top two cells, and the 0/1 lies flat at the bottom with its 1 completing the column and its 0 sliding into the teal sum-5 block. That block closes with the 2/3 flat — 2, then 3 — beside the two zeros already planted there.
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