The case notes
Reject a thermometer start that empties its box
This thermometer stays inside the centre box. The two fours outside the box remove four from every cell here except those on the thermometer. Watch a worked example, then try the idea in a puzzle.
Put it into practice
The box needs 4 on the thermometer
This thermometer stays inside the centre box. The two fours outside the box remove four from every cell here except those on the thermometer.
Try 5 at the bulb
What if the round bulb were five? The line must rise at every step. Four more cells would need at least six, seven, eight and nine.
No place for 4 in the box
That leaves no four anywhere on the thermometer. But every other cell in its box has already lost four. The box would be missing a digit.
Remove 5 from the bulb
So five cannot start this thermometer. We used the box requirement to rule out a bulb value that the thermometer alone would allow.
Read the transcript
This thermometer stays inside the centre box. The two fours outside the box remove four from every cell here except those on the thermometer. What if the round bulb were five? The line must rise at every step. Four more cells would need at least six, seven, eight and nine. That leaves no four anywhere on the thermometer. But every other cell in its box has already lost four. The box would be missing a digit. So five cannot start this thermometer. We used the box requirement to rule out a bulb value that the thermometer alone would allow.
