2 puzzles from Hugo Steinhaus, each explained in a minute and credited to the original work. Free on Savvy.
Take any three solid shapes, scattered anywhere in space, in any sizes — say, the bread, ham and cheese of an oddly assembled sandwich. Is there always a single flat plane that sli…
— Hugo Steinhaus and Stefan Banach, Ham sandwich theorem
Two people want to share a cake, but neither trusts the other to cut it fairly, and there's no outside referee to measure exact halves. Neither has to value every part of the cake …
— Hugo Steinhaus (with Stefan Banach and Bronisław Knaster), Fair Cake-Cutting