Sam's Basketball Conjecture

My son Tchapo and I were visiting my Peace Corps buddy Marek in Penn Yann, New York, a few years back. Greg, another Peace Corps buddy, was also visiting. The four of us were outside shooting hoops on Marek's basketball court, along with Marek's five-year-old son Sam. There were several balls flying around, and Sam was like a pinball under the basket, randomly careening about. We tried to keep the balls from hitting him, but ultimately someone took a shot and the ball came down on Sam's head.

After comforting the crying boy, we prepared to resume our shooting. Sam wanted to know, however, who threw up the ball that hit him. So he asked me: "Andy, did you throw that ball?"

"No, Sam," I replied truthfully. He turned to Greg: "Greg, did you throw the ball that hit me?" Greg also truthfully denied any involvement. He asked Tchapo: "Did you throw that ball?" Tchapo also denied putting that ball in the air. Sam persisted, and asked his daddy if he'd thrown the ball. Marek also truthfully denied it.

Sam was obviously puzzled for a moment, as his wheels and gears churned the data. Then, striking upon the only reasonable possibility, Sam asked his father: "Daddy, did I throw that ball?" In spite of the fact that he wasn't capable of heaving that ball, it seemed the only reasonable alternative, given the information he'd gathered.

He (like Sherlock Holmes) had exhausted all other possibilities, so the only one left - no matter how crazy - had to be the correct answer; except that Sam had forgotten (or was just discovering) that not all humans are truthful!

Sam tried a proof by exhaustion, and came up against a brick wall.


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