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In Devarim 1:15 (also Shemot 18:21) we see the numerical system of the hierarchical system of leaders:

ואקח את־ראשי שבטיכם אנשים חכמים וידעים ואתן אתם ראשים עליכם שרי אלפים ושרי מאות ושרי חמשים ושרי עשרת ושטרים לשבטיכם

So I took your tribal leaders, wise and experienced men, and appointed them heads over you: chiefs of thousands, chiefs of hundreds, chiefs of fifties, and chiefs of tens, and officials for your tribes.

Why the extra level of 50, and not simply 10-100-1000-10,000 (or at least 10-100-1000-shevet)?

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    Surmising - 600,000 people. Divided by 50 makes 12,000. 12 tribes leaves 1,000 of them per tribe. One of the qualifications was Anshei Chayil - men of war. When Moshe sent warriors to fight Midian he sent 12,000 warriors; 1,000 per tribe. – DanF Jul 27 '18 at 15:56
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    You should quote Shmot first: ואתה תחזה מכל-העם אנשי-חיל יראי אלוהים, אנשי אמת--שונאי בצע; ושמת עליהם, שרי אלפים שרי מאות, שרי חמישים, ושרי עשרות. כב ושפטו את-העם, בכל-עת, והיה כל-הדבר הגדול יביאו אליך, וכל-הדבר הקטון ישפטו-הם; והקל, מעליך, ונשאו, איתך. as that was Yitroh's advice, and that also says Judges explicitly. – Al Berko Jul 27 '18 at 16:12
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    @DanF The 600,000 people were not evenly distributed between the 12 tribes. – Alex Jul 27 '18 at 16:27
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Some say that the captains of thousands and hundreds were primarily military leaders (cf. Numbers 31:14), while the captains of fifties were primarily Torah teachers and elders (cf. Isaiah 3:3; Adereth Eliahu; HaKethav VeHaKabbalah).

(Living Torah Dev. 1:15)

The Torah is not writing in a less orderly way, or adding some ‘extra level’ of 50, it is indeed recording what it was. So, there were 12,000 ministers, each over 50. (600,000/50=12,000)

SAN. 18A:

תנו רבנן (שמות יח, כא) ושמת עליהם שרי אלפים שרי מאות שרי חמשים ושרי עשרות שרי אלפים שש מאות שרי מאות ששת אלפים שרי חמשים שנים עשר אלף שרי עשרות ששת ריבוא נמצאו דייני ישראל שבעת ריבוא ושמונת אלפים ושש מאות: The Sages taught: The verse states: “And place over them ministers of thousands, ministers of hundreds, ministers of fifties, and ministers of tens” (Exodus 18:21). The number of ministers of thousands was 600, as there were 600,000 men in total; the number of ministers of hundreds was 6,000; of ministers of fifties, 12,000, and of ministers of tens, 60,000. Therefore, it is found that the total number of judges of the Jewish people was 78,600, and suitable people were found to fill all of these positions.

Yad Ramah adds, that the final number above, 78,600 were not part of the 600,000.

ש"מ דהני שרים כולהו לבד משש מאות אלף רגלי דחשיב קרא נינהו

If they’d be included, you’d need to subtract 131 from every thousand among the 600,000 (which would be the 78,600). Meaning to say, they were indeed a separate number and group of people. See the rest for his complete calculation.

דאי ס"ד בכלל הנך נינהו הרי אתה צריך להוציא לכל אלף מאה ושלשים ואחד שרים.

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    Does this explain why there was a division into fifties at all? – Alex Jul 27 '18 at 18:29

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