Paper clippings

Paper clippings

We cut a sheet of paper into four pieces. Then we take one or two or three or the four pieces (at our choice) and again we divide them each into four pieces. We continue this way as many times as we want, always cutting into four pieces some or all of the resulting pieces of previous partitions at each step.

How many steps will we need at least to get 59 bits?


Each time we split a piece of paper, we increase the total number of pieces by 3 units. As we had started from a single unit (the sheet of paper), the resulting number will always be a multiple of 3 plus one. To check if a number meets this condition, simply divide it by three and see if the residue is 1. 59 does not meet it. Thus it will not be possible to obtain 59 pieces With the method described.