Are there opinions that permit adults to do a puzzle on shabbos and what is the accepted minhag?
The accepted minhag is not to make puzzles on Shabbos. This is the opinion of most poskim, although there are opinions that it is permitted, most poskim don’t permit it.
Ohr L’ztion 2-42(6) is lenient, However Yesodei Yisurun 2-pg. 52, Shmiras Shabbos Khichoso 16 ftnt.67, Shulchan Shlomo 340-13b,Shvus Yitzchok 1 g, 27, Tiltulei Shabbos pg. 25. ftnt 24, Nishmas Shabbos 340- 108,109,110,Shamlei Nissan- Dinei Kosaiv -1-2.