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In 1920, methodically-minded men within the war ministry of the new German republic imposed a systematic series of numerical designations on the army being formed from the wreckage of the forces of the old empire. This scheme provided the relatively small force being formed with a simple, and remarkably consistent, system of nomenclature At the same time, it was sufficiently flexible to accommodate the many new units and formations that would be formed in the course of any subsequent expansion of the modest military establishment allowed by victorious Allies.
The Reichsheer, as the new army was called, consisted of seven infantry divisions and three divisions of cavalry. Each of the infantry divisions took its number from that of the military region (Wehrkreis) in which it was based. Thus, the 1st Infantry Division was based in Military Region 1 (Königsberg) and the 7th Infantry Division in Military Region 7 (Munich.)
Within each division, singleton units, such as the one artillery regiment, bore the number of that division. Infantry regiments, of which there were three in every division, bore numbers derived from a set of three simple formulas.
The number given to the junior infantry regiment in each division was found by multiplying the number of the division by three. Thus, the infantry regiment of the 1st Infantry Division with the highest number was the 3rd Infantry Regiment. Likewise, the junior infantry regiment of the junior division of the entire force was the 21st Infantry Regiment of the 7th Infantry Division.
The other two infantry regiments in each division bore numbers calculated by subtracting one or two from the number of the junior regiment. Thus, the three infantry regiments of the 2nd Infantry Division were the 6th, 5th, and 4th Infantry Regiments.
Plans for the eventual expansion of the seven infantry divisions into an army worthy of a major European power often began with the trebling of existing units and formations. Thus, each infantry division would create two copies of itself, thereby turning an array of seven such formations into a force of twenty-one.
To provide numbers for the new divisions, the drafters of expansion plans added standard figures, whether ten or twenty, to the designation of the formation being duplicated. Thus, while the senior daughter division of the 4th Infantry Division would be called the 14th Infantry Division, her younger sister would become known as the 24th Infantry Division.
To find numbers for new infantry regiments, the planners used a different system. To provide a number to the senior duplicate of each existing regiment, they added twenty-one to the designation of the original. To provide a number for each junior duplicate, they added forty-two.
The protocol for naming new divisions had sufficient flexibility to accommodate the creation of two new military districts. Thus, in 1935, when the German authorities created the 8th Military Region (Wehrkreis VIII), they experienced no trouble finding numbers for the infantry divisions, whether real or imagined, affiliated with that district.
The scheme for numbering new infantry regiments was not so flexible. Thus, a new system had to be introduced. This second system, in turn, fell apart when, in order to provide infantry regiments for the infantry divisions of two additional military regions (Wehrkreis IX and Wehrkreis X), the German authorities began to move infantry regiments from one division to another.
Source: Gliederung der Truppen des Heeres ab 15.10.1935, Russisch-deutsches Projekt zur Digitalisierung deutscher Dokumente.