Also known as the Book-Stacking Problem. Simon had tried to build this tower at the Fries Museum where we visited a huge Escher exhibition (to the annoyance of the museum staff, to whom I had to explain that it was a serious math experiment and not just a kid dropping bricks), but it only worked with 4 blocks (possibly because the blocks were made of foam and weren’t rigid enough). He tried to stack the blocks on top of one another, shifting every next block first by one eighth, then by one sixth, next by one fourth, and next by one half – in the end, the top block would no longer be positioned above the bottom block.
He repeated the experiment at home, first doing some calculations and then using more rigid wooden blocks and managed to stack a tower of 6 blocks! (The top block still overlapped the bottom one by a bit though) :