The problem involves calculating permutations with restrictions. Initially, there are 4! = 24 possible 4-digit numbers using digits 1, 2, 3, 4 without repetition. The restrictions significantly reduce this number. Restriction 4 (1 is not at the first place) eliminates numbers starting with 1. Restriction 3 (4 is not at the last place) eliminates numbers ending with 4. Further constraints like '2 and 3 are not to immediately follow each other' and '1 is not to be immediately followed by 3' require careful exclusion of specific permutations. Calculating the valid numbers requires systematic enumeration or the principle of inclusion-exclusion, accounting for all given conditions simultaneously.