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i've never heard of a puzzle record
Most of them are ancient 10" shellac 78s. They're multigrooved with each track on its own groove, so when the needle is placed on the record there is no telling which song is going to play. Having researched a bit (by which I mean looking at discogs, ebay listings, youtube) a lot of the oldest ones tell you the songs on each side, but then in the 20s and 30s there are some which play up the 'puzzle' element by saying quizzing things on the label like 'This side contains 3 tunes. Can you find them?', or ones which may list the songs in bulk but not tell you which side to find them on, that's for you to trial and error repeatedly.
The limerick one is the only one I can find so far to contain both and inner and outer grooves with their own parallel grooves. 'Puzzle' indeed.
https://www.youtube.com/watch?v=LIPHT3R1Dsg
Some puzzle plates were also non-musical, instead being games with different horse racing or football results in the grooves and you play along with an accompanying playing card to see who will win, effectively like a board game. These were around in the 20s and 30s and then - as mentioned upthread - the horse racing style was revived as a proper board game in the 70s.
https://www.youtube.com/watch?v=FRRsweVLv-c
― you can see me from westbury white horse, Monday, 26 September 2022 16:20 (one year ago) link