05 / NINE PANES, TWO WITNESSES
Before you spoke
The glass is transparent. The useful part is what they cannot see.
Nine panes have been taken from a glasshouse. Each bears one bird and one kind of glass:
| Bird | Glass |
|---|---|
| Lark | amber |
| Wren | amber or blue |
| Swift | amber or blue |
| Swan | amber or clear |
| Owl | blue or clear |
Each bird–glass pair is one distinct pane: nine possibilities in all. One pane is chosen and kept fixed.
Mira is told only its bird. Ivo is told only its glass. Both know the whole table, what the other has been told, and that both reason correctly. They hear each statement before making the next. There are no coded signals or extra clues.
- Mira “I cannot tell which pane it is.”
- Ivo “I knew that before you spoke.”
- Mira “Now I can tell.”
- Ivo “Now I can too.”
Which pane was chosen? Explain what each speaker can rule out.
Keep a shortlist
Leave a pane checked while you consider it possible. Uncheck it when you can explain why it cannot fit. This is your working list; it does not mark answers right or wrong.
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A little assistance
Hint 1 — open only if wanted
Is any bird paired with only one kind of glass?
Hint 2 — open only if wanted
Put yourself in Ivo’s place before the conversation starts. Could he have been told amber and still been certain Mira would not know?
Hint 3 — open only if wanted
After amber is excluded, which bird still has two possible panes?
Hint 4 — open only if wanted
Of the three panes left after Mira knows, which kind of glass identifies just one?
Reveal the solution and its reasoning
The chosen pane bears a swan in clear glass.
- Mira’s first line excludes the amber lark: a person told “lark” would know immediately. Eight possibilities remain publicly.
- Ivo knew Mira would be uncertain before she spoke. If he had been told “amber,” he would originally have considered the lark possible. He could not then have known she would be uncertain. His glass is blue or clear.
- Five possibilities remain: blue wren, blue swift, clear swan, blue owl, clear owl. Mira can identify the pane, so her bird cannot be owl. The shortlist becomes blue wren, blue swift, clear swan.
- Ivo can identify it too. Blue would still leave him choosing between wren and swift. Clear leaves only swan.
No probabilities or guesses are needed. Knowing the pane is stronger than making a lucky correct guess.
A second look
Replace only Ivo’s second line with “I know that now.” Can the remaining conversation still be truthful under the same rules?
Reveal what the changed line does
No pane fits the altered conversation. “I know that now” adds nothing beyond Mira’s public admission. It does not say Ivo knew anything about her uncertainty beforehand.
After Mira’s first line, each remaining bird still has two kinds of glass. Her own admission teaches her nothing new, and Ivo’s weaker line adds no distinction. Her subsequent “Now I can tell” cannot be true.
A tense can carry more than a decorative change of weather.
Bring the step that changed your mind
A shortlist is welcome. So is the exact line where you stopped trusting it. If you share a full answer, say so first for readers still solving.
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