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- Impossible_Puzzle abstract "The Impossible Puzzle, also named Sum and Product Puzzle is a puzzle called "impossible" because it seems to lack sufficient information for a solution. It was first published in 1969 by Hans Freudenthal, and the name Impossible Puzzle was coined by Martin Gardner. The puzzle is solvable, though not easily. There exist many similar versions of puzzles.".
- Impossible_Puzzle wikiPageExternalLink 55655.html.
- Impossible_Puzzle wikiPageExternalLink impossible_puzzle.html.
- Impossible_Puzzle wikiPageExternalLink sumproAusAI.pdf.
- Impossible_Puzzle wikiPageExternalLink logic_sum_product.
- Impossible_Puzzle wikiPageExternalLink freudenthal1.pdf.
- Impossible_Puzzle wikiPageID "11066851".
- Impossible_Puzzle wikiPageRevisionID "600214782".
- Impossible_Puzzle content "P knows p=30. P suspects , , and . P knows s is 17, 13, or 11. If s=17: :S would suspect , , , , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." If s=13: :S would suspect , , , , and . :S would know if , P would know the numbers. :S would not be able to say "I was sure that you could not find them." If s=11: :S would suspect , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." Therefore, when S says "I was sure that you could not find them," P eliminates but cannot decide between and .".
- Impossible_Puzzle content "P knows p=42. P suspects , , and . P knows s is 23, 17, or 13. If s=23: :S would suspect , , , , , , , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." If s=17: :S would suspect , , , , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." If s=13: :S would suspect , , , , and . :S would know if , P would know the numbers. :S would not be able to say "I was sure that you could not find them." Therefore, when S says "I was sure that you could not find them," P eliminates but cannot decide between and .".
- Impossible_Puzzle content "P knows p=60. P suspects , , , , and . P knows s is 32, 23, 19, 17, or 16. If s=32: :S would suspect , , , , , , , , , , , , , and . :S would know if or , P would know the numbers. :S would not be able to say "I was sure that you could not find them." If s=23: :S would suspect , , , , , , , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." If s=19: :S would suspect , , , , , , , and . :S would know if , P would know the numbers. :S would not be able to say "I was sure that you could not find them." If s=17: :S would suspect , , , , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." If s=16: :S would suspect , , , , , and . :S would know if or , P would know the numbers. :S would not be able to say "I was sure that you could not find them." Therefore, when S says "I was sure that you could not find them," P eliminates , , and but cannot decide between and .".
- Impossible_Puzzle content "P knows p=66. P suspects , , and . P knows s is 35, 25, or 17. If s=35: :S would suspect , , , , , , , , , , , , , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." If s=25: :S would suspect , , , , , , , , , , and . :S would know if , P would know the numbers. :S would not be able to say "I was sure that you could not find them." If s=17: :S would suspect , , , , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." Therefore, when S says "I was sure that you could not find them," P eliminates but cannot decide between and .".
- Impossible_Puzzle content "P knows p=70. P suspects , , and . P knows s is 37, 19, or 17. If s=37: :S would suspect , , , , , , , , , , , , , , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." If s=19: :S would suspect , , , , , , , and . :S would know if , P would know the numbers. :S would not be able to say "I was sure that you could not find them." If s=17: :S would suspect , , , , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." Therefore, when S says "I was sure that you could not find them," P eliminates but cannot decide between and .".
- Impossible_Puzzle content "P knows p=72. P suspects , , , , and . P knows s is 38, 27, 22, 18, or 17. If s=38: :S would suspect , , , , , , , , , , , , , , , , and . :S would know that if , P would know the numbers. :S would not be able to say "I was sure that you could not find them." If s=27: :S would suspect , , , , , , , , , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." If s=22: :S would suspect , , , , , , , , and . :S would know if or , P would know the numbers. :S would not be able to say "I was sure that you could not find them." If s=18: :S would suspect , , , , , , and . :S would know if or , P would know the numbers. :S would not be able to say "I was sure that you could not find them." If s=17: :S would suspect , , , , , , and . :S would know that P would not know the numbers. :S would be able to say "I was sure that you could not find them." Therefore, when S says "I was sure that you could not find them," P eliminates , , and but cannot decide between and .".
- Impossible_Puzzle content "See Mathematician P's actual reasoning above.".
- Impossible_Puzzle hasPhotoCollection Impossible_Puzzle.
- Impossible_Puzzle header "Case 1".
- Impossible_Puzzle header "Case 2".
- Impossible_Puzzle header "Case 3".
- Impossible_Puzzle header "Case 4".
- Impossible_Puzzle header "Case 5".
- Impossible_Puzzle header "Case 6".
- Impossible_Puzzle header "Case 7".
- Impossible_Puzzle headerstyle "text-align:left".
- Impossible_Puzzle subject Category:Puzzles.
- Impossible_Puzzle type Abstraction100002137.
- Impossible_Puzzle type Communication100033020.
- Impossible_Puzzle type Message106598915.
- Impossible_Puzzle type Problem106784003.
- Impossible_Puzzle type Puzzle106784639.
- Impossible_Puzzle type Puzzles.
- Impossible_Puzzle type Question106783768.
- Impossible_Puzzle type Subject106599788.
- Impossible_Puzzle comment "The Impossible Puzzle, also named Sum and Product Puzzle is a puzzle called "impossible" because it seems to lack sufficient information for a solution. It was first published in 1969 by Hans Freudenthal, and the name Impossible Puzzle was coined by Martin Gardner. The puzzle is solvable, though not easily. There exist many similar versions of puzzles.".
- Impossible_Puzzle label "Impossible Puzzle".
- Impossible_Puzzle label "Luzifer-Rätsel".
- Impossible_Puzzle label "Onmogelijke Puzzel".
- Impossible_Puzzle sameAs Luzifer-Rätsel.
- Impossible_Puzzle sameAs Onmogelijke_Puzzel.
- Impossible_Puzzle sameAs m.02qzwnn.
- Impossible_Puzzle sameAs Q1878412.
- Impossible_Puzzle sameAs Q1878412.
- Impossible_Puzzle sameAs Impossible_Puzzle.
- Impossible_Puzzle wasDerivedFrom Impossible_Puzzle?oldid=600214782.
- Impossible_Puzzle isPrimaryTopicOf Impossible_Puzzle.