The Puzzle Thread

[leonid]

My take on cabinet puzzle

The first man's cabinet is labeled either AAA or AAO
The second man's cabinet is labeled either AAO or AOO

Case 1: The third man said yes -> his cabinet is labeled either OOO or AOO
Case 1.1: The first man's cabinet is labeled AAA

cabinet| 1 | 2 | 3 | 4 |
label  |AAA|   |   |   |
content|   |   |   |   |

cabinet| 1 | 2 | 3 | 4 |
label  |AAA|   |   |   |
content|AAO|   |   |   |
Cabinet #1 contains two apples and can't be AAA

cabinet| 1 | 2 | 3 | 4 |
label  |AAA|AAO|   |   |
content|AAO|AOO|   |   |
Cabinet #2 contains one apple and one orange and can't be AAO

cabinet| 1 | 2 | 3 | 4 |
label  |AAA|AAO|AOO|   |
content|AAO|AOO|OOO|   |
Cabinet #3 contains two oranges and can't be AOO

cabinet| 1 | 2 | 3 | 4 |
label  |AAA|AAO|AOO|OOO|
content|AAO|AOO|OOO|AAA|

Case 1.2: The first man's cabinet is labeled AAO

cabinet| 1 | 2 | 3 | 4 |
label  |AAO|   |   |   |
content|   |   |   |   |

cabinet| 1 | 2 | 3 | 4 |
label  |AAO|   |   |   |
content|AAA|   |   |   |
Cabinet #1 contains two apples and can't be AAO

cabinet| 1 | 2 | 3 | 4 |
label  |AAO|AOO|   |   |
content|AAA|AAO|   |   |
Cabinet #2's label can't be AAO
Cabinet #2 contains one apple and one orange

cabinet| 1 | 2 | 3 | 4 |
label  |AAO|AOO|OOO|   |
content|AAA|AAO|AOO|   |
Cabinet #3's label can't be AOO
Cabinet #3 contains two oranges

cabinet| 1 | 2 | 3 | 4 |
label  |AAO|AOO|OOO|AAA|
content|AAA|AAO|AOO|OOO|

We can't tell the cabinet's contents if the third person said "yes" because there are two possible outcomes


Case 2: The third man said no -> his cabinet is labeled either AAA or AAO

cabinet| 1 | 2 | 3 | 4 |
label  |   |AOO|   |   |
content|   |   |   |   |
Label AAA and AAO must be taken by cabinet #1 and #3 in some order,
So cabinet #2's label can only be AOO

cabinet| 1 | 2 | 3 | 4 |
label  |   |AOO|   |   |
content|   |AAO|   |   |
Cabinet #2 contains one apple and one orange and can't be AOO

cabinet| 1 | 2 | 3 | 4 |
label  |   |AOO|   |   |
content|AAA|AAO|   |   |
Cabinet #1 contains two apples and can't be AAO

cabinet| 1 | 2 | 3 | 4 |
label  |AAO|AOO|AAA|   |
content|AAA|AAO|   |   |
Cabinet #1's label can't be AAA

cabinet| 1 | 2 | 3 | 4 |
label  |AAO|AOO|AAA|OOO|
content|AAA|AAO|   |   |

cabinet| 1 | 2 | 3 | 4 |
label  |AAO|AOO|AAA|OOO|
content|AAA|AAO|OOO|   |
Cabinet #4 can't be OOO

cabinet| 1 | 2 | 3 | 4 |
label  |AAO|AOO|AAA|OOO|
content|AAA|AAO|OOO|AOO|

Third person said "no" and we figured out the cabinet's contents with 100% certainty