The Maximal number of floors a Building can have where you can tell the highest floor from where you can throw a glass ball without breaking it, if you have b glass balls and are allowed t throws is Σ1 ≤ i ≤ b binomial(t,i)

By Shalosh B. Ekhad

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Written: Nov. 7, 2010.
This apparetly ancient brain-teaser (but an internet search only lead to the special case of two glass balls (and 100 floors)) was kindly brought to my attention, via my master, by Nati Linial.

! ת ו ד ה   ר ב ה   נ ת י   ל י נ י א ל

Added Nov. 16, 2010: Doron Zeilberger, my beloved master, just told me that I got scooped by Michael Boardman (Mathematics Magazine, Vol. 77, No. 5 (Dec., 2004), pp. 368-372), except that he was dropping eggs rather than glassballs.
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