How to pick some numbers out of 13 integers, from an 4 digits code

[batmath]

This is the question I read in a Math quizzes book:

• you have the first 13 integers from 1 to 13
• someone gives you a code made of at most 4 digits (0 to 9)
• you decipher the code and tell him exactly which numbers he wanted from the list
• each number can be picked only once

For example.
case 1 He gives you 8191 and you tell he thought all the 13 integers from 1 to 13.
case 2 He gives you 6145 and you tell he thought only 1, 2, 13.
And so on.

I've not come up with any solutions yet. The only sparse ideas I have are:
case 1 if you sum the first 13 integers you get 91, so the last two digits of 8191
case 2 if you sum 1, 2, 13 you get the same result summing the digits of 6145

Also,
8191 mod 3 = 13
6145 mod 2 = 3

Beside that , I have no other clues how to move forward.
I would be grateful for some hints how to go on. Thank you very much.

 

[khansaheb]

8191 mod 3 = 13
6145 mod 2 = 3

How did you calculate these? Please share your work.

 

[Steven G]

This is the question I read in a Math quizzes book:

• you have the first 13 integers from 1 to 13
• someone gives you a code made of at most 4 digits (0 to 9)
• you decipher the code and tell him exactly which numbers he wanted from the list
• each number can be picked only once

You didn't mention anything about someone wanting any numbers from a list. I can only assume that the list is from 1 to 13(?????)

In the red above you mentioned him. Is this him the same person whom gave you the code??

 

[Dr.Peterson]

This is the question I read in a Math quizzes book:

• you have the first 13 integers from 1 to 13
• someone gives you a code made of at most 4 digits (0 to 9)
• you decipher the code and tell him exactly which numbers he wanted from the list
• each number can be picked only once

For example.
case 1 He gives you 8191 and you tell he thought all the 13 integers from 1 to 13.
case 2 He gives you 6145 and you tell he thought only 1, 2, 13.
And so on.

Hint 1: How many possible requests (sets of integers) could someone make?

Hint 2: Convert 8191 and 6145 to binary.