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I was reminded of this by my discussion with John in the comments to Lecture 11.
In 1969 the Mathematician Hans Freuden came up with the following puzzle:
\(A\) says to \(S\) and \(P\): I have chosen two integers \(x\), \(y\) such that \(1 < x < y\) and \(x + y ≤ 100\). In a moment, I will inform \(S\) only of \(s = x + y\), and \(P\) only of \(p = xy\). These announcements remain private. You are required to determine the pair \((x, y)\). He acts as said. The following conversation now takes place:
i. P says: “I do not know it.”
ii. S says: “I knew you didn’t.”
iii. P says: “I now know it.”
iv. S says: “I now also know it.”
Determine the pair \((x, y)\).
(translated from Dutch by van Ditmarsch et al. here)
I think this puzzle is cute, hopefully someone here might find it fun too.