- #1

robertphy

- 11

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- TL;DR Summary
- How to pick some numbers out of 13 integers, by a 4 digits code

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.

And so on.

I've not come up with any solutions yet. The only sparse ideas I have are:

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.

- 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 6145Also,

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.