The case notes
Work inwards from both ends of a thermometer
The bulb is three, and the tip is six. The two cells between them are empty. We can work out both by reading the thermometer from each end. Watch a worked example, then try the idea in a puzzle.
Put it into practice
3 → ? → ? → 6
The bulb is three, and the tip is six. The two cells between them are empty. We can work out both by reading the thermometer from each end.
From the bulb: at least 4, then 5
Start at the bulb. Each step must go up by at least one. After three, this cell is at least four, and the next is at least five.
From the tip: at most 5, then 4
Now read backwards from six. The cell before it is at most five. The one before that is at most four. Both bounds meet.
3 → 4 → 5 → 6
So the middle cells are four and five. A fixed digit at either end can squeeze a thermometer until only one value fits each cell.
Read the transcript
The bulb is three, and the tip is six. The two cells between them are empty. We can work out both by reading the thermometer from each end. Start at the bulb. Each step must go up by at least one. After three, this cell is at least four, and the next is at least five. Now read backwards from six. The cell before it is at most five. The one before that is at most four. Both bounds meet. So the middle cells are four and five. A fixed digit at either end can squeeze a thermometer until only one value fits each cell.
