Math Question I really don't know how to solve?

Question

Please show me step by step!

Write an eight-digit number using the digits 1,2,3 and 4 twice so that the 1s are separated by 1 digit, the 2s are separated by 3s digits, and the 4s are separated by 4 digits.

Just Me nope that not what i meant!

Runner wrong answer that not what the book says!

Answer 1

The number is 41312432.

The "4" is in the 1st anf fifth space. 4_ _ _ _4_ _
The "1" is in the 2nd and 4rth space_1_ 1_ _ _ _
The "3" is in the 3rd and 7th space _ _ 3_ _ _3_
The "2" is in the 5th and 8th space_ _ _ _ 2 _ _2

Don't know any way to show steps other than the way I did here...

BTW the number 23421314 also satisfies the requirements.

Answer 2

the 1 should be separated by one digit, so you will have a portion that will appears like: 1N1. Do the same with other numbers:
2NNN2, 4NNNN4
Now you need to combine this bits:

You're not given instructions for the 3, so you might put then anywhere but first, start with what you're given.

1N1 it's the first part. It's a three number combination that it's also what you need between the "2", so you get so far:

21N12

You need the 4 with four numbers between them so you can'place them next to the each "2"s. Place one where the N is:

21412.

You have so far 5 numbers already and you need three more: 4 and the two 3's.

If you put a 4 next to any of the 2's you will get them separate by two numbers only, and you need to get them separated by four. So, put the 3s and then, the 4:

21412334 or
43321412

There you have.

Answer 3

4 1 3 1 2 4 3 2
4 _ _ _ _ 4 _ _ 4 digits between the 4s
_ 1 _ 1 _ _ _ _ 1 digit between the 1s
_ _ 3 _ _ _ 3 _ 3 digits between the 3s
_ _ _ _ 2 _ _ 2 2 digits between the 2s

Is this what you meant?

Answer 4

43321412

4 _ _ _ _ 4 _ _ 4 digits between the 4s
_ _ _ _ 1 _ 1 _ 1 digit between the 1s
_ _ _ 2 _ _ _ 2 3 digits between the 2s

Self-explainatory