KenKen — 5×5
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6+
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4
12×
6+
4-
4+
7+
8+
5+
5+
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6+
Research Clues
About hard KenKen
Five-by-five grids with all four arithmetic operations. Division cages add a new constraint layer — a "2÷" cage can only hold factor pairs like (4,2) or (2,1). Multiplication cages can have surprisingly few valid combinations once you account for the digit range.
The key insight at this level: single-cell cages are free information. Fill those first, then propagate through their row and column. After that, focus on cages with the fewest possible combinations. You'll uncover forced digits that cascade through the rest of the grid.