from the Australian Intermediate Mathematics Olympiad:
Hello, delicate_tears!
Let = number of 6-, 10-, and 15-passenger taxis, respectively,
. . where: .
We have: .
. . Hence: . .[1]
Since is an integer, .
. . Then [1] becomes: .
Since , then: .
It seems that there are: . possible choices.
However, if , then . . . not allowed.
Therefore, there are ways.