Can you solve it? The club sandwich problem

A multi-layered brain snack

UPDATE: The solutions are now posted here.

Here are two puzzles I ordered on room service.

1) A number sandwich is a line of digits such that there is one digit sandwiched between the 1s, two digits sandwiched between the 2's, three digits sandwiched between the 3's, and so on. For example, 312132 is a number sandwich with the digits 1,2 and 3