Eli5. Why do military groups (101st airborne for example) seem to be numbered in random order
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As several people have already explained how many of these units were originally sequentially numbered, I will just add to that by explaining another few reasons for gaps or seemingly really high numbers with countries besides the US.
Many countries have air forces that were originally formed under the British Royal Air Force, either as part of the Commonwealth or as part of governments-in-exile during WW2. These squadrons were numbered as part of an overall RAF system of numbering where these government-in-exile squadrons received numbers in the 300s and squadrons formed under the Commonwealth Air Training Plan were numbered in the 400s. When the war ended and these squadrons returned home, many kept their numbers and retained the legacy, and in some cases formed the basis of the numbering system for their new Air Force. Like the Greeks took No. 335 and 336 Squadrons home with them, and now the Hellenic Air Force flying squadrons are numbered in the 320s-350s.
Similar to this are the units of the countries which became independent of the Soviet Union. Many of these simply retained their Soviet-era numbers (although there has been a drift towards renumbering over time as some of these countries seek distance from their Soviet past).
Then you have units that are (or were) part of a numbering system, but that system isn’t a simple 1 to whatever. The system assigns block ranges to units of a certain type or origin, like the US Army divisions or Royal Air Force and Fleet Air Arm squadrons. So Fleet Air Arm squadrons were numbered in sequence, but the numbers were in the 800s to keep them all together but without duplicating any RAF squadron numbers. And US Army infantry divisions immediately before WW2 were 1-25 for the Regular Army, 26-45 for the National Guard, 63-106 were Organized Reserve. Cold War expansion of the National Guard added 46-52 to their number range.
Finally, you have numbering systems where the number is based on information about the unit, like its mission, recruitment area, or even its base. So recruiting district 3 may form regiments 31, 32, etc. During WW2, the Italian Army gave its tank divisions numbers starting with 131, paratrooper divisions numbers in the 180s, and coastal defense divisions in the 200s. For the last one, an example is the Republic of Singapore Air Force where the support squadrons are numbered such that the last digit is the air base, so the units at Changi Air Base are 208, 508, 608, 708, 808 (this is also an example of the first digit being based on the mission of the unit, where the second digit is the only one that goes in sequential order.)
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