🔧 Step-by-Step Answer Walkthrough For Easy Level
The teal less 1 block in the bottom-left corner holds three cells, and every one of them must stay below 1 — which in pip terms means 0, the only value that fits. Two of those cells stand stacked in the block's left-hand column, so the 0/0 double takes them: 0 in the upper cell, 0 in the lower cell. The orange less 1 singleton at the bottom-right is asking for a 0 as well; it just has to wait for a different tile.
The purple equals column at the top-right is three cells that must all match. The 5/5 double claims the two upper cells, 5 in the top one and 5 in the middle one. That leaves the column's bottom cell needing the same value — and after the double is spent, the only tile left in the tray carrying a matching pip is the 5/0.
Stand the 5/0 vertically: 5 up in the bottom cell of the purple column, 0 down in the orange less 1 cell at the bottom-right corner. That single placement closes the equals column and satisfies the last less-1 region in the same stroke — the reason Livengood's small boards feel so tidy.
The third teal cell, out to the right of its block, still needs a 0, and the 0/1 is the last tile with one to offer: lay it flat with 0 on the left in the teal block's top-right cell and 1 on the right in the lower cell of the pink equals pair. Pink now wants a partner 1, which the 3/1 provides from the row above — 1 on the right in the pink pair's upper cell, 3 on the left in the uncoloured free square, the one cell on this board with no rule attached.
🔧 Step-by-Step Answer Walkthrough For Medium Level
The purple sum 1 cell in the top-left admits exactly one pip: 1. The tray has a single tile carrying a 1, the 2/1, and it stands vertically in the left column — 1 up in the purple corner, 2 down in the uncoloured square directly beneath it. One tile placed, and 1 is now off the table for every other region.
The teal less 3 pair in the bottom-left insists that both of its cells stay under three. The purple greater 3 singleton sits immediately to its left and demands the opposite — something above three. The 4/0 answers both, lying flat: 4 on the left in the purple greater 3 cell, 0 on the right in the lower cell of the teal pair, legal only because teal tolerates anything below three.
With 0 and 1 already used, the only pip left under three is a 2, so the teal pair's upper cell must be a 2. That means the 2/3 stands vertically through that slot: 2 down in the teal pair's upper cell, 3 up in the pink greater 2 singleton above it, comfortably clearing a clue that only asks for more than two. Teal now reads 2 over 0 and is finished.
Two doubles remain in the tray. The green sum 4 pair in the bottom-right is a vertical slot filled by one tile, so its halves must be equal and add to four — only the 2/2 can do that, 2 in the upper cell and 2 in the lower. The orange equals pair across the centre is a horizontal slot needing a double of its own, so the 3/3 stands vertically through it, 3 in the left cell, 3 in the right, with its lower half lodging in the uncoloured square below.
The blue sum 7 pair still needs filling, and by now only the 5/3 and the 2/0 are unused. Five plus two makes seven, so the 5/3 lies flat with its 5 on the right in the blue pair's upper cell and its 3 on the left in the right cell of the orange equals pair, completing that trio of 3s. The 2/0 closes the board along the bottom row: 0 on the left in the uncoloured square, 2 on the right in the blue pair's lower cell.
🔧 Step-by-Step Answer Walkthrough For Hard Level
Two regions here are single cells asking for a sum of 0, and pips never go negative — each can only hold a 0. The tray carries exactly two tiles with a zero, the 0/5 and the 3/0, so both are accounted for before anything else moves. The 0/5 stands vertically with its 0 up in the green sum 0 cell at the centre and its 5 down in the left half of the pink sum 9 pair directly beneath. The 3/0 lies flat out on the right: 0 in the teal sum 0 cell, 3 in the uncoloured square immediately to its left.
The blue equals block down the left side needs three identical pips. Its top two cells sit side by side, which is a double's job: the 6/6 lies flat, 6 in the top-left cell and 6 in the top-right. The block's third cell tucks below the top-right one, and the 2/6 reaches it — 6 on the left going into that bottom-right cell of the block, 2 on the right going into the lower cell of the green sum 6 pair beside it.
The green sum 6 pair now reads 4 over 2, because its lower cell was taken by the 2 on that last tile and the upper must therefore be a four. The 4/3 lies flat through it: 4 on the left in the green pair's upper cell, 3 on the right in the purple sum 3 singleton next door. Two regions close at once, and the equals block is complete at three matching pips.
The pink sum 9 pair already holds a 5 in its left half, courtesy of the very first tile placed. Its right half therefore needs a four, which the 4/5 supplies standing vertically — 4 up in the pink pair's right cell, 5 down in the left cell of the orange sum 6 pair. That leaves the orange pair wanting a 1 in its right cell, and the 2/1 brings it, also standing vertically: 2 up in the teal sum 2 singleton, 1 down in the orange pair's right cell.
Now work across the crowded centre, where single-cell targets sit in a line. The purple sum 4 and the pink sum 4 are shoulder to shoulder, an obvious berth for the 4/4 double lying flat with 4 in each half. Further right the teal sum 6 and the orange sum 4 are neighbours, and the 6/4 lies flat between them: 6 on the left in the teal cell, 4 on the right in the orange cell. To their left the orange sum 5 and the blue sum 3 pair up on the 3/5 — 5 on the left in the orange cell, 3 on the right in the blue cell.
Up in the top-right the purple sum 6 cell has the pink less 2 cell directly below it, and that vertical stack takes the 6/1 standing upright: 6 in the purple cell, 1 in the pink less 2 cell, comfortably under two. Along the bottom, the blue less 7 pair is the natural berth for the remaining double, the 3/3 lying flat with 3 in each half, and the green sum 5 pair takes the 4/1 flat alongside — 4 on the right, 1 on the left.
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