Day of the year: count on 1, 2, 3...10. Formula?

Question

bash

Good day!
Depending on the day of the year 1...365, select one of 10 directories. How to pay for the first or second at the physical, then pay for the first ... tenth.
Is there a formula? Or will it be necessary to decompose into arrays in a cycle from 1..365?
PHP array example:
[1] => [1, 11, 21, n1],
[2] => [2, 12, 22, n2],
[3] => [3, 13, 23, n3],
[4] => [4, 14, 24, n4],
[5] => [5, 15, 25, n5],
[6] => [6 , 16, 26, n6],
[7] => [7, 17, 27, n7],
[8] => [8, 18, 28, n8],
[9] => [9, 19, 19, n9],
[10] => [10, 20, 30, n10],
Without an array using a formula, can you somehow calculate in one step?
Sincerely,
Alexey.

Answer 1

Division with remainder - look at the math textbook for grade 3.