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The title "What is the numbering system used for the DSN dishes?" pretty much sums it up.

DSN dishes are referenced by seemingly arbitrary numbers: 14, 55, 36, etc... Do these numbers carry any specific significance? How were they assigned?

Screenshot from https://eyes.nasa.gov/dsn/dsn.html

Looking at the history of DSN on Wikipedia, it appears that the tens-place digit originally was allocated to identify the region or site, and within a region/site the dishes were numbered sequentially as they came online, but some have been retired while others continued in operation, so the numbering is today a little irregular.

In 1966, Goldstone California had dishes 11, 12, 13, 14; two sites in Australia were 41 and 42; South Africa had 51, Madrid 61, and Canaveral and Ascension (an island in the Atlantic) were 71 and 72.

Over the years the DSN sites were consolidated down to three: Canberra, Madrid, and Goldstone.

When Canberra ran out of numbers in the 40s, apparently they were allocated the 30s as well; likewise Goldstone got the 20s, and Madrid got the rest of the 50s. I think within each decade the antennas are generally numbered more or less sequentially in construction order.

I found a sort of explanation in "Uplink-Downlink" the NASA history of the DSN.

The first digit [range of digits, really, see the table] gives the geographical area.

The second digit gives the antenna number within that geographical area. Sometimes the second digit is consistent for an antenna type (23, 33, 53 are OVLBI) but not always.