A bag holds two counters, black or white — Carroll claimed you could find their colors
Lewis Carroll's final and most argued-over 'pillow problem': a bag contains two counters, each independently either black or white, with no other information given. Carroll offered a chain of reasoning that appeared to pin down the counters' colors anyway, purely from probability, without ever opening the bag or drawing one out.
Reveal the answer
Carroll's own 'solution' is a trick: it's a flawed argument dressed up as valid probability, and the actual colors genuinely cannot be determined from the information given. Mathematicians still debate exactly which step in Carroll's reasoning smuggles in an unjustified assumption; the puzzle is now used as a teaching example of how easily probabilistic reasoning can go wrong even when every individual step looks plausible.
— Lewis Carroll (Charles Dodgson), Pillow Problems — Problem No. 72, 1893
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