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I worked for Control Data Norway from 1985 through 1990 and for Control Data Germany from 1991 through mid 1995. The actual Time Sheet form I scanned has some notes on it (which I obscured) which I think is from December 1990 or January 1991.

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Quis custodiet ipsos custodes?

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Preposition usage is a minefield for foreigners, in many languages:
at six o'clock, on Tuesday, in the third week of May!

By the way, in future I recommend you ask what is idiomatic or natural, rather than 'correct': you want to know how people actually speak, not how their Latin teachers urged them to speak or write a hundred years ago. (I used to teach linguistics, so I'm allergic to prescriptivism).

For your first question, I recommend in even-numbered weeks only. "On a week" doesn't feel right to me at all, all the more so because a week is too long to be treated as a point in time, in most circumstances. And in a week means you're free to do it any time during that week. Also, the hyphen helps show the phrasing, to avoid mistaking even for an adverb (auch). By the way, I'm sure I've seen diaries in the UK with the weeks numbered.

On the use of only, remember that language doesn't follow the same tidy rules as logical formulae. With the best will in the world, some sentences with only will still be ambiguous or clunky: in these cases, rephrase altogether.

I enjoy these interesting questions about idiom. Bring them on.

cheers

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Joe

Joe-Casey,

Thanks a lot for your comments and excellent explanation of why "in even-numbered weeks" is better than "on even-numbered weeks".
I googled for "in/on odd/even-numbered weeks". Here the somewhat surprising result:

"in even-numbered weeks":  158 hits
"on even-numbered weeks":  321 hits
"in odd-numbered weeks":   648 hits
"on odd-numbered weeks":   226 hits

Please feel free to correct and comment on any interesting English errors I make in my posts. I want to improve.
Over the years I have realized how important it is to be able to express myself clearly, precise and unambiguously in writing.
Sometimes it is absolutely crucial that the reader, when reading what I have written, conceives exactly the same meaning from the text as I.

SURE.
Especially in languages with few cases like English and Norwegian, where prepositions have replaced cases like accusative and dative.

Correct spelling is also pretty important. Here a true picture of a board found on the street in front of a kiosk in downtown Oslo a couple of years ago.

What they wanted write was: "We have pizza in the freezer."  (NO: "Vi har pizza i frysern.")   [Correct Norwegian: "Vi har pizza i fryseren."]
What the board says is:     "We have peed in the freezer."   (NO: "Vi har pissa i frysern.")

No real Norwegian words have the letter Z in them. Only imported foreign words.

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Quis custodiet ipsos custodes?

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Pleased to hear my comments help. To be strictly accurate, I can only offer a rationalisation for the "in a week" usage: I wouldn't want anyone to belive that idiom can always be explained: often it defies explanation.
Your google survey is interesting, and we ought to find a graduate student who can follow these up and see if there's a geographical pattern. I wouldn't be astonished if an American replies here to say that on a week sounds perfectly natural there.

cheers

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Joe

No, if someone said that here in the U.S., we would think that they were either from another country or drunk. I suspect that most of the google hits Børge found were nothing but typographical errors.

@Børge re: the pizza in the freezer: I thought only lazy Americans (not all Americans are lazy) did stupid stuff like that!

I have been in email contact with a former CDC colleague, who worked in R&D in Arden Hills, Minneapolis from September 1969 through 1996. I asked him if they in the US had to fill out a Time Sheet similar to the one used in Europe, and if it ever had a week number field.

Here his answer, which hopefully clarifies things:
Regarding the backup program used in the "good old days of large CDC mainframe computers":
This was not a program made centrally by CDC development. The one we used for the customers in Norway was locally developed in Norway in a script (command shell) programming language called CCL (Cyber Control Language).
For each customer it was customized to that customer's special needs.

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Quis custodiet ipsos custodes?

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Wow! He just missed my father! He worked at the Minneapolis facility from late 1966 or early 1967 to about December of 1968, when his health necessitated a move to Arizona. As they say, small world!

When I worked for CDC, I visited the CDC facilities in and around Minneapolis, but only during summer (July/August), and it was definitely too hot for me. But I assume it can get pretty could during the winter.

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Quis custodiet ipsos custodes?

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