Seen previously. Kim has $10$ identical lamps and $3$ identical tables. How many ways are there for her to put all the lamps on the tables?

One lamp on each table I believe

Only the number of lamps on each table matters, so we can list the possibilities systematically: / begin{align*}

(&10,0,0) / /

& (9,1,0) / /

& (8,2,0) / /

& (8,1,1) / /

& (7,3,0) / /

& (7,2,1) / /

& (6,4,0) / /

& (6,3,1) / /

& (6,2,2) / /

& (5,5,0) / /

& (5,4,1) / /

& (5,3,2) / /

& (4,4,2) / /

& (4,3,3)

/end{align*}There are a total of $/boxed{14}$ possibilities.