温度计数独
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9
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9
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如何玩温度计数独
标准数独规则适用。附加规则：沿着每条灰色温度计的数字必须从灯泡（圆形端）到尖端严格递增。一个3单元格温度计可以是2,5,8或1,4,9，但不能是3,3,7或5,4,8。
完整指南 →
Digits 必须沿着 thermometer shapes 严格递增
什么是温度计数独？
Thermo Sudoku在网格上叠加thermometer shapes。每个thermometer在一端有一个bulb（圆形），另一端有一个tip。沿着任何thermometer的数字必须从bulb到tip严格递增。结合标准Sudoku约束，这产生了强大的推理链——知道bulb至少为1，tip至多为9，你可以根据每个单元格在thermometer上的位置计算其有效值范围。
一览
| 约束类型 | 线条约束 |
| 典型给定数 | 20–28 |
| 难度评级 | ★★★★☆ 4/5 |
| 平均解题时间 — 简单 | 10 分钟 |
| 平均解题时间 — 中等 | 22 分钟 |
| 平均解题时间 — 困难 | 45 分钟 |
| 平均解题时间 — 专家 | 75 分钟 |
如何解温度计数独
| 技巧 | 它的作用 | 级别 |
|---|---|---|
| Range Restriction from Length | A thermometer with N cells must use N strictly increasing distinct values. The bulb is at least 1 and the tip is at most 9, giving a calculable valid range for each cell. | 高级 |
| Minimum/Maximum Bounding | The bulb value is ≤ 9 − (N − 1). The tip value is ≥ N. Apply these bounds immediately to prune all thermometer candidates. | 高级 |
| Overlapping Thermometer Deduction | Two thermometers sharing a cell give tighter combined bounds than either alone. | 高级 |
| Forcing Chains via Thermometers | When a value is forced into a thermometer cell, all cells closer to the bulb must be smaller and all closer to the tip must be larger. | 高级 |
| Short vs. Long Thermometers | A 2-cell thermometer is simply a greater-than relationship. A 9-cell thermometer forces exactly 1–9 in order. | 高级 |
平均解题时间
简单
10 分钟
中等
22 分钟
困难
45 分钟
专家
75 分钟
常见问题
什么是温度计数独？
Thermo Sudoku is a variant where thermometer shapes are drawn on the grid. Each thermometer has a bulb (rounded end) and extends through several cells toward a tip. The digits must strictly increase from the bulb to the tip — so every cell along a thermometer must hold a larger digit than the one before it.
如何阅读 thermometer clues？
The bulb is the starting point and must hold the smallest digit on that thermometer. Each subsequent cell must be strictly larger. For example, a 3-cell thermometer starting at the bulb means the bulb holds at most 7 (since two larger digits must follow). A 5-cell thermometer means the bulb holds at most 5.
Can digits repeat on a thermometer?
No. Because digits must strictly increase, no digit can appear twice on the same thermometer. A 4-cell thermometer uses four different increasing digits. Combined with standard Sudoku uniqueness rules, thermometers create very tight constraints on every cell they pass through.
Is Thermo Sudoku hard to learn?
The core rule is simple — digits increase from bulb to tip. Beginners can start solving after understanding just that one constraint. What makes higher difficulties challenging is tracking minimum and maximum values for each thermometer cell simultaneously across many overlapping thermometers.
What is the best first move in Thermo Sudoku?
Look for long thermometers. A 7-cell thermometer can only start at 1 and end at 7, 8, or 9 — drastically limiting all seven cells. Also check for thermometers where the bulb or tip overlaps with a constrained row, column, or box, as this often pins the starting digit immediately.
How long does Thermo Sudoku take to solve?
Easy puzzles take 8–15 minutes. Medium puzzles typically run 15–30 minutes. Hard puzzles average 35–60 minutes and expert puzzles can exceed 90 minutes. The difficulty scales sharply as thermometer lengths decrease and the number of simultaneously active constraints increases.