Matching Pairs - Column To Automatically Populate With Any Of 3 Digit Numbers That Share Two Numbers

This is what I need:

Columns B, C, D & E are all populated with 3 digit numbers.

I would like column F to automatically populate with any of the 3 digit numbers that share two numbers, i.e.

F2 might look like this (using 00 as the pair):

001, 040

F3 might look like this (using 01 as the pair):
701, 051, 110, 001, 120

F4 might look like this (using 12 as the pair):
123, 721, 281, 912, 112, 120

etc...