🔧 Step-by-Step Answer Walkthrough For Easy Level
The teal greater-4 cell on the left edge can only take a pip higher than four. Scan the tray: a single tile carries such a pip, the 5/2. It has to stand vertically against the left edge, because the only cell touching the teal cell is the purple equals pair's left cell above it. So 5 drops into the teal gate and 2 rises into the purple pair — and that means the purple pair's right cell is a 2 as well.
The purple pair's right cell needs a 2, and the only remaining tile with a 2 is the 2/1. That cell's only other neighbour is the pink pair's left cell, so the 2/1 tile lies flat across the boundary between the two equals pairs: 2 in the purple pair's right cell, 1 in the pink pair's left cell. The pink pair now repeats 1, which means its right cell is a 1 too.
The pink pair's right cell is a 1, and its only untouched neighbour is the orange less-4 cell below it. The 0/1 tile is the piece that fits: it stands vertically with 1 rising into the pink pair's right cell and 0 dropping into the orange cell, which happily satisfies the less-than ruling.
Two tiles are left, the 1/3 and the 3/3. The green sum-1 cell at the centre of the board must hold a 1, so the 1/3 tile lies flat with 3 in the upper cell of the blue sum-6 pair and 1 in the green cell. The blue pair now needs 3 more in its lower cell, and the 3/3 double supplies it: the double lies flat along the bottom with 3 in the blue pair's lower cell and 3 in the uncoloured square. Final board: purple reads 2+2, pink reads 1+1, blue reads 3+3, teal holds 5, orange holds 0, green holds 1, and the free square holds 3.
🔧 Step-by-Step Answer Walkthrough For Medium Level
The teal sum-1 block in the middle of the board spans three cells. Three pips adding to one means two of them are the floor value and one carries the whole total. Only two tiles in the tray contain a floor-valued half — the 0/1 and the 4/0 — so both are committed here, and the block's remaining job is to find which of its cells takes the odd pip.
Two regions want a total of ten from two pips: the pink pair at the top and the purple pair at the bottom-right. Ten can be built as 5+5 or 6+4, and the tray has exactly one 6, sitting on the 3/6 tile, whose partner is a 3 — useless for making ten. So the top pink pair cannot use a 6 with a 4 partner from that tile alone; instead the 5/5 double is reserved for the bottom-right purple pair, and the top pink pair must take the 6 with a 4 supplied by a second tile.
The 6 must sit in the pink pair's left cell, so the 3/6 tile's 3 goes to its only other neighbour: the upper cell of the purple equals pair at the top-left. The purple pair repeats, so its lower cell is also 3 — and the only tile that can feed that cell from below is the 3/1, standing vertically with 3 up and 1 down in the left cell of the orange equals pair. The 4 for the pink pair comes from the 4/0 tile, standing vertically at the top row's right end: 4 in the pink pair's right cell, 0 down into the teal block's top-left cell.
The orange pair repeats, so its right cell is a 1, and the 0/1 tile lies flat between orange and teal: 1 in the orange pair's right cell, 0 in the teal block's bottom-left cell. The teal block now holds two zeros and needs its total, so its bottom-right cell takes the 1 of the 2/1 tile — the 2 half crossing right into the blue equals block. That makes the blue block's value 2, and the 2/2 double stands vertically to fill its top-right and bottom-right cells.
The green sum-6 pair at the bottom is filled by the 3/3 double standing vertically, with 3 in its upper cell and 3 in its lower cell. The final tile is the 5/5 double, which lies flat in the bottom-right purple sum-10 pair — 5 in the left cell, 5 in the right cell. All three of the tray's doubles have now sealed a pair or a block, and the totals read 6+4 on pink, 0+0+1 on teal, 1+1 on orange, 2 three times on blue, 3+3 on green and 5+5 on the bottom-right purple.
🔧 Step-by-Step Answer Walkthrough For Hard Level
There are two pink sum-0 cells — one at the top of the board above the orange sum-9 pair, one out on the top-right edge — and both must read 0. The purple sum-6 cell in the top-right corner must read 6. The corner cell has exactly one neighbour, the teal equals block's top-left cell, so whichever tile carries the 6 must also drop a pip into the block.
Inside the teal equals block, the top-right and middle-right cells share a single tile, and since all four block cells must match, that tile has to be a double. The right-edge pink 0 cell has only one neighbouring cell, the block's bottom corner, so its tile must be one of the four zero-carrying tiles and its other half must equal the block's value. The block's value therefore has to appear both as a double and as the partner of a zero tile. Only the 1/1 double qualifies, so the block reads 1 everywhere.
With the block set to 1, three tiles fall immediately. The 6/1 stands vertically at the top-right corner, 6 in the purple sum-6 cell and 1 down in the block's top-left cell. The 1/1 double stands vertically inside the block, filling its top-right and middle-right cells. The 1/0 lies flat at the block's bottom corner, 1 in the block's bottom-right cell and 0 out to the right in the pink sum-0 cell.
The orange sum-9 pair above the purple equals block cannot be satisfied by one tile: nothing in the tray carries 6 with 3 or 5 with 4, so nine is built as 5+4 by two tiles meeting inside the pair. The 0/5 stands vertically on the top pink sum-0 cell, 0 up and 5 down in the pair's left cell. The 4 comes from the 4/2, standing vertically with 4 up in the pair's right cell and 2 down in the purple block's top cell — so the whole five-cell block reads 2, with the 2/2 double standing vertically in its middle-right and bottom-right cells.
The green sum-12 pair at the centre needs both its cells at the top of the range, and the 6/5 supplies the first: 6 up in the green pair's left cell, 5 down in the purple sum-14 block's top-right cell. The 6/2 supplies the second, 2 up in the purple equals block's bottom-centre cell and 6 down in the green pair's right cell. The blue sum-1 cell takes the 1 of the 4/1, whose 4 drops into the sum-14 block's top-left cell, and the 5/3 completes the sum-14 block: 5 up in its bottom-right cell, 3 down in the pink sum-6 run's left cell. The sum-14 block now reads 4+5+5.
The green equals pair on the left reads 4 twice: the 0/4 lies flat with 0 in the blue less-8 pair's right cell and 4 in the green pair's upper cell, while the 3/4 lies flat with 4 in the green pair's lower cell and 3 in the orange equals pair's upper cell. The orange pair repeats, so its lower cell takes the 3 of the 3/2, which lies flat with its 2 ending up in the purple equals block's bottom-left cell. The last tile, 1/2, lies flat in the bottom run: 2 in its middle cell and 1 in its right cell, giving 3+2+1 for the sum-6 run. Finally the blue less-8 pair is filled by the 3/0 standing vertically at the left edge, 0 up in its left cell and 3 down in the teal sum-3 cell.
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