404: The Address That Survived
A Manyfold mystery
404: The Address That Survived
Rook's Manyfold Directory recovered four suggestions for a vanished page: PATH, MOTH, MASH, and MATE. The missing address has exactly four letters. An address may be any four letters; it does not have to be a word. Each suggestion differs from the missing address in exactly one position.
Rook's report
Four near matches. No exact page.
- suggestions
- 4
- exact pages
- 0
- letters
- 4
| 1 | 2 | 3 | 4 |
|---|---|---|---|
| P | A | T | H |
| M | O | T | H |
| M | A | S | H |
| M | A | T | E |
“Missing is not the same as unknowable.”
Vivian
Turn the page to inspect Rook's recovered report.
Read the report. Test the evidence.
Recover the address, then test every three-clue case.
Every suggestion differs from the missing address in exactly one position.
2 / 3
Keep the evidence in view
The complete report
All four rows are aligned by letter position.
1. Recover the address
Write and circle directly on this page.
What address vanished? Write it in the address field. Then circle the one letter in each suggestion that does not match your address.
2. Prove the any-three claim
Use this page and scratch paper as needed.
Rook claims that if any one suggestion is lost, the other three still prove the same missing address. Is Rook correct no matter which suggestion is lost? Explain how you know.
Explain why your conclusion covers every possible lost suggestion.
The boundary case
When two clues are not enough
Every address below still has four letters. It may be any four letters; it does not have to be a word.
Same rule
Each retained suggestion must be exactly one position away.
Finish the proof
Record every requested conclusion here.
3 Find the ambiguity. Prove the minimum.
Keep only PATH and MATE. Find every four-letter address that is one letter away from both. Use this pair and Part 2 to determine the fewest suggestions Rook must keep to guarantee that the missing address can still be proved, no matter which suggestions remain.
Every address that works:
Fewest suggestions that guarantee recovery:
Why this is the minimum:
4 Build one more suggestion.
Write one more familiar four-letter word that Rook could suggest for the missing address. It must not be one of the four suggestions already listed. Show which one letter changed.
The changed position is .
