Tentaizu Strategy Guide

Tier 1: Immediate Deductions (Always Check First)

The Zero Rule

Any cell showing 0 has zero mines in all eight neighbors. Mark every unknown neighbor as safe (✓) immediately. This is the fastest deduction in the game and often cascades — a newly-safe cell may be adjacent to another constrained clue that now resolves.

The Eight Rule

Any cell showing 8 has a mine in every one of its eight neighbors. Flag all of them (💣) at once. An 8 in the center of the board instantly accounts for 8 of the 10 mines — a massive head start.

Satisfied Constraints → Safe Neighbors

When a numbered cell already has exactly as many mine flags around it as its number, all remaining unknown neighbors are definitively safe. Mark them ✓. This is arguably the most-used deduction in the game; re-check every clue whenever you place a new flag.

Forced Mines (Pigeonhole)

When a numbered cell's remaining mine count equals its number of unknown neighbors, every one of those neighbors must be a mine. For example: a cell showing 3 already has 1 flag, leaving a mine count of 2 — and exactly 2 unknown neighbors remaining. Both unknowns are mines. Flag them immediately.

Tier 2: Constraint Arithmetic

Constraint Subtraction

This is the most powerful intermediate technique. When two number cells share some (but not all) of their unknown neighbors, you can subtract one constraint from the other to learn about their exclusive neighbors.

Example: Cell A has value 2 and three unknown neighbors — two shared with cell B and one exclusive to A. Cell B has value 1 and two unknown neighbors (both shared with A). Because B's single mine must be one of the two shared cells, A's exclusive neighbor is responsible for exactly 2 − 1 = 1 mine. You now know A's exclusive cell is a mine without directly seeing it confirmed.

Practice spotting overlapping clue regions. Any time two clues share a neighbor subset, subtraction may reveal hidden information.

Set Inclusion

A stronger version of subtraction: if cell A's unknown neighbors are a strict subset of cell B's unknown neighbors, then B's mines include all of A's mines plus some extras. Specifically:

• B_value − A_value = number of mines in B's exclusive neighbors.
• If B_value = A_value, B's exclusive neighbors are all safe.
• If B_value − A_value = number of B's exclusive neighbors, all of B's exclusive neighbors are mines.

This deduction appears frequently near edges and corners where neighbor sets overlap heavily.

Tier 3: Global Mine Counting

The Running Tally

Always track how many mines you've flagged. Subtract from 10 to know how many remain. This global constraint becomes decisive late in the puzzle:

• 1 mine remaining, large unknown area: Often you can identify multiple cells that cannot be the last mine through existing clues, leaving only one candidate.
• 0 mines remaining: Every unflagged cell is safe. Mark them all ✓ and the puzzle is essentially solved.
• N mines remaining, N unknown cells total: Every unknown cell is a mine. Flag them all.

Counting Unknown Cells

Count the total number of cells that are still unknown (not flagged or marked safe). If this count equals the remaining mines, every unknown cell is a mine. If remaining mines = 0, every unknown is safe. These global deductions sidestep the need for local constraint analysis entirely.

Tier 4: Advanced Patterns

The 1-2-1 Pattern

Three cells in a row along an edge, showing 1-2-1, with unknown cells above (or below), is a classic Minesweeper pattern that applies equally to Tentaizu. The two outer clues (1 and 1) each have exactly one mine among their respective exclusive neighbors, forcing the mine of the middle clue (2) to lie in the shared center neighbor. This resolves all three clues at once.

The 1-2-2-1 Edge Pattern

Along a board edge, 1-2-2-1 in a row means the two middle cells share mines in a symmetric way. The two outer 1s constrain where mines can be in the middle pair's exclusive cells. Combined with the global count, this often forces the entire strip.

Corner Cell Logic

Corner cells have only 3 neighbors. A corner clue of 3 means all three neighbors are mines — even if none of the other clues point there yet. A corner clue of 2 with one flag placed means both remaining neighbors split: one is the mine, one is safe — determine which using adjacent clues.

Speed Strategies for Faster Times

• Scan before touching. Before placing a single flag, scan the whole board for 0s, 8s, and obviously satisfied constraints. Building a mental map first prevents backtracking.
• Work from the most constrained areas outward. Corners and edges resolve fastest. Solve the periphery, then let those deductions cascade inward.
• Use the mine counter actively. Glance at remaining mines after every flag. Late-game, the counter alone often collapses the puzzle.
• Practice recognizing satisfied constraints immediately. Train yourself to spot — at a glance — when a clue's flag count matches its number. This is the most frequently applicable deduction and the one that separates fast solvers from slow ones.
• Don't mark safe cells unless they help. Marking ✓ is optional — only do it when it helps you visually track progress. Excessive marking slows you down.

When You Feel Stuck

If you've applied all the above techniques and still can't make progress, try these approaches:

1. Re-examine every satisfied constraint. A newly-placed flag may have satisfied a clue you previously overlooked. Do a full re-sweep.
2. Look for overlapping clue pairs you haven't tried. Systematically apply constraint subtraction to every pair of adjacent numbered cells that share unknown neighbors.
3. Count all unknowns and compare to remaining mines. The global deduction catches cases that local analysis misses.
4. Remember: every Tentaizu puzzle is solvable. If you're genuinely stuck after all the above, there is a deduction you've missed — not a guess required. Stay calm and look again.