What was the reason for an odd number of astronauts in almost every group of the early US space program?

Question

We are familiar with the first groups of NASA astronauts, like the Mercury Seven and the New Nine. Something about that struck me as (literary) odd; All the first twelve astronaut groups had an odd number of astronauts, except for Astronaut Group 3 and 4. The probability for such a coincidence is quite low, so there was perhaps a reason for this policy.

Why did NASA hire an odd number of astronauts in almost all the first astronaut groups?

7 , 9 , 14 , 6 , 19 , 11 , 7 , 35 , 19 , 17 , 13 , 15

Edit:

For comparison, the same pattern does not exist in the Soviet space program. A list of the cosmonaut groups can be found here.

Answer 1

Can't answer the overall question, but for Group 1 specifically, there's a discussion of the recruitment program here. The original plan was to recruit twelve, to allow for some dropping out during the program. When it became clear there were unlikely to be many dropouts, they revised the target to six. However, when making the final selection, they got stuck on bringing the shortlist down to 6:

Sitting in judgment over 18 finalists, Donlan, White, and North pared down the final pool of selectees, choosing each to complement the rest of the group. The going was so difficult that they could not reach the magic number six, so Gilruth decided to recommend seven. Donlan then telephoned each of the seven individually to ask whether he was still willing to accept a position as a Mercury astronaut. Each one gladly volunteered again.

So that one's as much an accident as anything...

(edit:) Group 4 was originally six strong, but one (Graveline) resigned before being assigned to a mission.

(edit:) Group 7 was essentially arbitrary - it was "all the Manned Orbiting Laboratory astronauts under 35". It so happened there were an odd number of them, but there was no set number initially aimed for.

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After accounting for these, we end up with:

1. Planned even, actually odd (7)
2. Odd (9)
3. Even (14)
4. Even (6)
5. Odd (19)
6. Odd (11)
7. No plan for numbers, actually odd (7)
8. Odd (35)
9. Odd (19)
10. Odd (17)
11. Odd (13)
12. Odd (15)
13. Odd (23)
14. Even (24)
15. Odd (23)
16. Even (44)
17. Even (32)
18. Odd (17)
19. Odd (11)
20. Even (14)
21. Even (8)

So across all 21 groups, and taking account of the fact we know two were intended to be different sizes, this is eight even, twelve odd, one "whoever happens to qualify" (but happened to be odd). This certainly feels like there's no intentional focus on odd numbers.

Answer 2

It's not that much of a coincidence -- about 1 in 52 for 10 or more odd numbers out of 12. You would have been just as surprised by ten or more even numbers, so you can bring that down to 1 in 26. And you would have been just as surprised to see such a discrepancy in the Soviet space program, instead of the US program, so you can bring it down to 1 in 13.

To sum up: your claim that there "must have been a reason for this policy" is unfounded.

Answer 3

Richard Feynman:

You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight?

Amazing!

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Based on the excellent answer by @TokyK let's look at the numbers with python:

even_odd = [[(i/2**n)%2 for n in range(12)] for i in range(2**12)]

sums = [sum(x) for x in even_odd]

A, B = np.histogram(sums, bins = range(14))

list(A) 

[1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1]

4096. / (1 + 12 + 66 + 66 + 12 + 1)

25.924050632911392

So chances are 1 in 26 that there are two or less groups that are even or odd.

What are the chances that - considering all of the things that happened in the Apollo space program - one of them had a chance of 1 in 26 or less of happening?

Essentially 100%.

Per day?

Essentially 100%.

Per person?

Essentially 100%.

Stuff happens.

Answer 4

I can't remember who told me this. But I've heard that the reason astronauts go up in odd numbers is so they don't form "teams" against each other. For example, if six astronauts spend a year in space together, three astronauts might disagree with the three other astronauts on some problem. This would create a lot of tension with no easy way to solve the problem. But if seven astronauts were to go up, opinions would never be split evenly. A decision would always have a deciding vote, and everyone could move on.

I can't give a source right now. But that's what I've heard.