# How many ways one can put prime numbers to form 3 digit NIP?

1. Jun 16, 2017

### Mrencko

1. The problem statement, all variables and given/known data
as listed above the question is how many and which three digit NIP can be formed whit the use of prime numbers

2. Relevant equations
nothing currently trying to understand

3. The attempt at a solution
well i have found at least 168 primer numbers below 1000 i mean in the range of three digit,
and grouped in three groups:
numbers of 1 digit "4"
numbers of two digit "21"
numbers of three digit ""143"
as far i know this is a permutation because order matters so 717 is diferent of 177 and 771 so
i am thinking of like a billion of ways to put those numbers to form a NIP, my question is this is even doable?
how can i start to mix this to make to the final count of how many ways one can put all those numbers to form the NIPS
***** update: i think for the three digit numbers there is a rule of 3! on each one so making 6 ways to put that number so if i multiply that for 143 this gives me 858 ways in total but i dont know if this is correct, and its just for the three digit numbers
**** second update:
i permuted every 1 digit number whit every 2 digit number
11 and 2,3,5,7 ok then 112, 211,121. so 3!=6 then 6*4 the 4 represent the 1 digit numbers
24 is the total acoding to this so 24*21 21 represents the total 2 digit numbers, this gives to me
504 but previously i ve calculated the permutation of 3 digit numbers so using the prefix "and"
504*858=432432
i dont know if i am right can you help me?

Last edited: Jun 16, 2017
2. Jun 16, 2017

### WWGD

What is an NIP?

3. Jun 16, 2017

### Mrencko

i guees the number for the bank and things like that only uses numbers and not letters

4. Jun 16, 2017

### WWGD

Do you mean PIN, personal identification number?

5. Jun 16, 2017

### Mrencko

yes but in my homework says NIP

6. Jun 16, 2017

### WWGD

Can you find out how it is defined?

7. Jun 16, 2017

### Mrencko

is in spanish "numero identificacion personal" check my lastest update

8. Jun 16, 2017

### WWGD

Ok, did not expect Spanish with that username. Seems you have the option for 3, of 4P3= $\frac {4!}{1!}=4!=24$ with just one digit. Then you can have combinations of a 1-digit prime in the 1st, 2nd or 3rd spot and a two-digit prime in the remaining two spots ( if you allow this; maybe you just allow a 1-digit prime in spot 1 and a 2-digit prime afterwards or a 1-digit prime in spot 3 and a two-digit prime in the first two spots, and then consider all the 3-digit primes.

9. Jun 16, 2017

### Mrencko

so my analisis in the update its all right? or have some flaws

10. Jun 18, 2017

### Mrencko

my new doubt is if do i need to multiply the results?
i mean the 24 forms of the 1 digit numbers, the 504 form for the two digit numbers and 1 digit number and the 858 form of the three digit numbers?
24*504*858=?

11. Jun 19, 2017

### haruspex

This is too vague.
It could mean just using prime digits, or concatenating 1-, 2- and 3-digit primes.
I'm pretty sure it does not mean more convoluted uses like this:
If you allow that sort of thing then you can almost surely make every 3-digit number not ending in zero. Your multiply by 6 rule will in itself count duplicates, e.g.133 would be counted twice.

12. Jun 20, 2017

### WWGD

Yes, this is where I sort of got stuck. It seems to need a version of multinomial coefficients, you know, the Mississippi thing..

13. Jun 20, 2017

### WWGD

Look up multinomial coefficients. These help you answer, e.g., the number of permutations of a word like Mississippi ( with many repeats ) as $\frac {11!}{2!4!4!}$; 4 repeats for s, for for i and 4 for p.

14. Jun 20, 2017

### Mrencko

yes i also think this is too vague, i will keep working on this and keep you updated.

15. Jun 20, 2017

### haruspex

My best guess is that the question just means using prime digits.

16. Jun 20, 2017

### Mrencko

1 digit prime numbers?

17. Jun 20, 2017

### haruspex

Yes. If it does not mean that, my next guess is using 3-digit prime numbers and concatenating 1-, and 2-digit prime numbers in either order, but certainly nothing more complicated than that.

18. Jun 20, 2017

### Mrencko

Yes, I didn't tough about the repeating numbers in the 3 digit, ultimately I will ask my professor tomorrow and update, I only hope this don't come in the test

19. Jun 20, 2017

### haruspex

It doesn't matter about repeating digits in a three digit prime as long as you don't allow reordering its digits.
What makes my second guess complicated (and therefore unlikely) is that you have to avoid three digit and two digit primes that can be made from one digit primes.
E.g. you can make 223 as 2,2,3 or 2,23 or 223, but must only count it once.
I recommend you to take the simplest view, just using single digit primes, and answer that.