lets take an example:

There is K boxes (k=5). And N objects (N=6). pigeonhole-principle says that at least one Box contain r objects (r=2).Then

ceilOf(N/K) ≥ r

ceilOf(5/4) ≥ r

2 ≥ r // r=2 which is true

ceilOf(N/K) can be greater than r Here we take only least amount of objects

There is K boxes (k=5). And N objects (N=6). pigeonhole-principle says that at least one Box contain r objects (r=2).Then

ceilOf(N/K) ≥ r

ceilOf(5/4) ≥ r

2 ≥ r // r=2 which is true

ceilOf(N/K) can be greater than r Here we take only least amount of objects