A cavalry sergeant has 24 horses available which he needs to put on 6 carriages. So he needs to divide 24 by 6. He does the following calculation, based on knowing that 6 will go into 24 at least once, and that 6 times 3 is eighteen.

24 / 6 = 13.
$\ 6$
--
18


After considerable difficulty with implementing his solution he consults his lieutenant. The lieutenant checks the calculation:

13 * 6

18
$\ 6$
---
 24

Implementation of the result still remains elusive so they consult the colonel, who uses
a different method to check:

13

13

13

13

13

13

In adding this up, the colonel arrives at the following sequence of intermediate results:
3,6,9,12,15,18,19,20,21,22,23,24.