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    $\begingroup$ Oh, yes, thanks, i have to rethink, and retype... @JaapScherphuis $\endgroup$ Commented Aug 15, 2024 at 12:52
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    $\begingroup$ Your generalization doesn't quite work, because adding more pills requires you to adjust the size of the bins. The 56 bound relies on the bin sizes you established for 48 pills. Adding more pills changes the bound. $\endgroup$ Commented Aug 15, 2024 at 17:54
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    $\begingroup$ @user2357112 Oh, yes, i have a moving target, have to go down to $51$... Thanks for the comment! $\endgroup$ Commented Aug 15, 2024 at 18:06