๐จ SPOILER WARNING
This page contains the final **answer** and the complete **solution** to today's NYT Pips puzzle. If you haven't attempted the puzzle yet and want to try solving it yourself first, now's your chance!
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๐ฒ Today's Puzzle Overview
Ian Livengood's easy grid centers on a triple-equals region at top-left, forcing the [1,1] double domino as the only way to satisfy three identical pip values. This anchor propagates through a greater-5 cell at [2,0] that must be 6, linking the [6,2] domino, and a second equals region in the bottom-left that forces a run of 2s. The final sum-8 pocket in the lower right then locks the remaining placements with a net total of 8 from a [0,4] and [4,6] combination. The solving graph branches from the triple-equals root, with one branch resolving left-column constraints and the other handling the sum-8 cluster independently.
Rodolfo Kurchan's medium puzzle builds from a pair of equals regions: a two-cell equals in the top row that squeezes a [2,0] domino into place, and a second equals in the middle column that forces a matching pair. A standalone sum-5 requirement at [4,0] drives the bottom-left corner, while a less-4 region at [3,0] restricts the vertical domino. The structure interleaves empty cell constraints, allowing a [6,6] double to fill the upper-left area, and a sum-5 pair at [3,2]-[4,2] that completes the grid. The deduction web has two independent entry points: the top-right equals and the bottom-left sum-5, converging on the central column.
Rodolfo Kurchan's hard grid complexity arises from a dense web of sum-3 and sum-4 single-cell constraints. The equals region at [2,2]-[4,2] forces all three cells to be 6, immediately placing the [6,6] double vertically. A sum-3 region at [0,3]-[1,4] plus a sum-4 at [0,2] forms a tight cluster that demands precise pip counts. Additional sum-3 constraints at [3,0], [7,2], and greater/less restrictions on the right edge create a network of small numerical locks. The solving path must navigate simultaneous equal chainsโlike the equals at [6,1]-[6,2] for 5s and the equals at [6,4]-[7,4] for 2sโwhile satisfying single-cell sum targets that fan out from the central equal column. This NYT Pips hard puzzle is a layered constraint graph where each sum microregion interlocks with neighboring less/greater filters.
๐ก Progressive Hints
Try these hints one at a time. Each hint becomes more specific to help you solve it yourself!
๐จ Pips Solver
Click a domino to place it on the board. You can also click the board, and the correct domino will appear.
โ Final Answer & Complete Solution For Hard Level
The key to solving today's hard puzzle was identifying the placement for the critical dominoes highlighted in the starting grid. Once those were in place, the rest of the puzzle could be solved logically. See the final grid below to compare your solution.
Starting Position & Key First Steps
This image shows the initial puzzle grid for the hard level, with a few critical first placements highlighted.
Final Answer: The Solved Grid for Hard Mode
Compare this final grid with your own solution to see the correct placement of all dominoes.
๐ฌ Community Discussion
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