>be Aoi>have two logic-perfect robots, ROBOBAR and ROBOKOL>give them a 6x6 grid with stars (see attached image)>ROBOBAR is given ONLY the Row number>ROBOKOL is given ONLY the Column letter>They do NOT know each other's info initiallyThe Conversation:1. ROBOBAR: "I don't know where the Aoi Star is."2. ROBOKOL: "I don't know where the Aoi Star is."3. ROBOBAR: "I don't know where the Aoi Star is."4. ROBOKOL: "I don't know where the Aoi Star is."5. ROBOBAR: "We could keep doing this forever and neither of us would ever know."6. ROBOKOL: "Now I know where the Aoi Star is."Question: In which cell is the star? Explain the logic
>>16936604>1. ROBOBAR: "I don't know where the Aoi Star is."So it's not row 5.>2. ROBOKOL: "I don't know where the Aoi Star is."So it's not column C.>3. ROBOBAR: "I don't know where the Aoi Star is."So it's not row 1.>4. ROBOKOL: "I don't know where the Aoi Star is."So it's not column E.>5. ROBOBAR: "We could keep doing this forever and neither of us would ever know."So it's not row 3 or 6.>6. ROBOKOL: "Now I know where the Aoi Star is."This means it's F4,
>>16936605small correction, "We could keep doing this forever and none of us would know" eliminates row 3 and col A.
>>16936605what?
>>16936905It's very simple anonif the star was C5 ROBOBAR would instantly know because there's only one star with that row number, so you can eliminate that rownow there's only one star left in the C column, so if it was there ROBOKOL would instantly know, so you can eliminate thatKeep going until you run out of row/columns to eliminate and the robots would be stuck repeating "I don't know" at each otherat that point, from ROBOBAR's viewpoint there would 2 rows with 2 stars and 1 row with 3 star left, from ROBOKOL's viewpoint there would be 3 columns with 2 stars left.ROBOBAR calculated he could never know the answer, which means he knows it's on the row with 3 stars (row 4). Now that ROBOKOL knows that he can pinpoint it.
>>16936908hurp, there would be 2 columns with 2 stars and 1 column with 3 stars, ROBOKOL is as stuck as ROBOBAR before ROBOBAR admits the impossibility.
>>16936604It seems like Robobar is making a guess which a conjunction on "I don't know where the Aoi star is." and "Given this, I don't think you know can know where the Aoi star is." or put another way "I don't know where it is and I know given what I know that you don't know where it is either." It also seems premature, which indicates it's outside of row six otherwise A column is a possibility, so this leaves columns 2, 4. So Kol can only know it if the column is F, which leaves only 4F.