After doing quite a lot of (probably not fairly authorized) digging, I feel I’ve discovered the tough start of the issue.

The drawback appears to have developed in round 1940, from the M.I.T campus throughout World War II.
The precise creator seems to be unknown.

An early use of the issue was in 1981 in Rick Billstein’s ‘An issue fixing method to arithmetic for elementary faculty lecturers‘, wherein Rick Billstein makes use of the census-taker drawback when in Chapter 4, discussing ‘Integers and Number Theory’

On web page 216, the answer course of to the census-taker drawback is damaged down step-by-step, however there isn’t a indication of the place the puzzle was from, whether or not authentic or sourced.

(Page 215 comprises a small paragraph on the backside that offers the issue, but in addition doesn’t point out a supply).

Looking round, I discovered this from 2010 that revisits the Census-Taker drawback, and inside it, on web page 2 it says:

‘According to [1], the census-taker drawback originated throughout World War II. In
literature, it has appeared in numerous tales in a puzzle-ese fashion. As a outcome,
many number-theoretic issues with seemingly inadequate info have been
proposed in some journals.‘

In the references, [1] is ‘M.H. Greenbelt, Mathematical Entertainments, Crowell, 1965.‘ Doing a bit extra digging, it seems it is a e-book from 1965:

Sadly from right here, I’ve been unable to search out wherever which totally disclosed the contents. However, what I did handle to search out is this google books web page which exhibits small snippets of the paragraph containing a key phrase. Trying a number of key phrases finally led me to this snippet from Page 1:

‘One of few amusing issues to come back out of World War II was a brand new sort of mind tornado – the “census-taker” drawback. (The time and place of an issue are troublesome to specify. To the perfect of the creator’s data, this drawback was born on the M.I.T Campus in one of many battle…‘

I’ve been unable to discover a snippet of the second half of the paragraph however I’ll maintain attempting.

Finally some google ngrams, displaying the usage of ‘census taker’ over time in books:

You can see there’s a massive spike in each in 1940, which appears to be the start of the issue, and in addition in about 1970 which appears to be when it began to be printed a bit extra.

Overall it seems that the unique drawback got here from the Campus of the Massachusetts Institure of Technology in the course of the early Forties.

However, the issue itself grew to become very fashionable within the Eighties, showing in lots of mathematical writings, and once more within the 2000s, being requested about on many boards and nonetheless is to at the present time. Notably, the earliest discussion board put up involving this drawback that I may discover was right here in 1995, the place it was answered a 12 months later.

For related puzzles, you may search for ‘Number idea riddles’ on-line, and the vast majority of those you discover are prone to be basic issues as effectively. The census-taker drawback appears to be the unique, which gave start to many different concepts for different issues utilizing this concept.

Hope this helps! It was enjoyable to analysis.