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$\begingroup$ If Mike has a padlock to which Jane has a key, why doesn't he just lock the box with it? $\endgroup$
– Mad Physicist
Commented Apr 4, 2016 at 4:17
$\begingroup$ The assumption is explicitly disallowed by the problem spec: "The two of them have many padlocks, but none to which the other has a key." $\endgroup$
– Mathieu K.
Commented Mar 16, 2022 at 8:34

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