Im trying to figure out how to place a number of items into containers evenly but without splitting.
Easy example:
11 items, 2 containers
11/2 = 5.5
so even distribution would look like this (without splitting):
container 1 = 5 items
container 2 = 6 items
but of course as the numbers grow and divisions results in decimals its gets a bit more complicated
111 items, 4 containers
111/4 = 27.75
In this case how do i turn .75 into an even distribution?
what equation would be give me 3? the number of extra items that will need to be distributed to a different container?
container 1 = 27 items
container 2 = 28 items
container 3 = 28 items
container 4 = 28 items
Let's say you have $n$ items and $c$ containers. You can safely put $\lfloor n/c \rfloor$ items into each container, where $\lfloor x \rfloor$ is the floor of $x$, i.e., $x$ rounded down to an integer.
Therefore the number of remaining items to be distributed is $$n - c\left\lfloor \frac nc \right\rfloor.$$
In the example you gave, this would be $$111 - 4\left\lfloor \frac {111}4 \right\rfloor = 111 - 4(27) = 3.$$
Note that if $c$ divides $n$, then $\lfloor n/c \rfloor = n/c$, so the formula reduces to $$n - c\lfloor n/c \rfloor = n - c(n/c) = n - n = 0,$$ as expected.