MathDB

In the unit squares of a transparent

1 \times 100

tape, numbers

1,2,\cdots,100

are written in the ascending order.We fold this tape on it's lines with arbitrary order and arbitrary directions until we reach a

1 \times1

tape with

100

layers.A permutation of the numbers

1,2,\cdots,100

can be seen on the tape, from the top to the bottom. Prove that the number of possible permutations is between

2^{100}

and

4^{100}

. (e.g. We can produce all permutations of numbers

1,2,3

with a

1\times3

tape)
Proposed by Morteza Saghafian

Problem Statement