Given $|B| = 23$ and number of partitions $P=4$. We want to partition the given set $B = B_1\cup\dots\cup B_P$ so that every partition $B_i$ contains the same amount of elements where the remaining elements are assigned to $B_1, \dots, B_P$.
At the beginning every partition gets an entire number of elements:
$\lfloor|B| / P\rfloor = 5$
$|B|- \lfloor|B| / P\rfloor * P = 3$
And the remaining elements are distributed as follows
$|B_1| = 5 + \textbf{1}$
$|B_2| = 5 + \textbf{1}$
$|B_3| = 5 + \textbf{1}$
$|B_4| = 5 + \textbf{0}$
How can we calculate from the given information the remaining number of elements (Bold in the partitions)?
Now I have the answer. The number of elements in the partitions can be calculated using the following formula:
$|B_p| = \lfloor|B| / P\rfloor + sgn(\lfloor(|B| - \lfloor|B|/P\rfloor P)/p\rfloor)$
Example from above:
$|B_1| = \lfloor23 / 4\rfloor + sgn(\lfloor(23 - \lfloor23/4\rfloor 4)/1\rfloor)$
$|B_1| = 5 + 1$