From my exposure to Japan and its culture, it seems to me that they are very interested in puzzles. There’s sudoku and kakuro. Japanese console RPGs are renowned for their puzzles. Mysteries, especially those fashioned after the Golden Age where the puzzle was all, seem to be very popular there - e.g. locked room mysteries top literary lists and mystery manga.
Where does this interest come from, do you think?
I know in Japan there was a very, very popular console game for children based entirely on 3D logic puzzles involving blocks, mazes, etc. It was one of those programs designed to make your kid smarter 
Other than that… no clue.
So far as I am aware, Sudoku was popularised by Americans.
I’ve never lived with a Japanese family, but I’ve read thousands of manga, watched hundreds of anime, and lived in Japan for seven years. I can’t say that I ever saw any particular interest in puzzles.
The only popular mystery manga is Detective Conan, and I wouldn’t say that the mysteries are presented as puzzles to the reader. While you can often guess which of the three or four suspects is the culprit through rote repetition of treatment, Conan is more about figuring out “how” the culprit commited the crime, but they never really give you enough clues to figure it out yourself.
(Interestingly, there’s a second series of Detective Conan written by a different guy than the creator. His have better mysteries, which aren’t always murders, and Conan is a lot more humble and caring. It was interesting to see the differences.)
I lived there for two years and did not see any great interest in puzzles. In Japanese you cannot have cross -words or quite a few other word puzzles we have in English. There are Japanese word puzzles.
That’s not true, there are most certainly Japanese crosswords. Since they use the kana syllabaries there are many more short words than English crosswords but they exist nonetheless. Here’s a list of crossword magazines from Amazon. Like your write, though, there are also several other word puzzles. While you can easily find magazines dedicated to these games in bookstores, they’re not quite as ubiquitous as English games. They’re not in major newspapers, though for some reason, the monthly magazine Nikkei Money has a crossword puzzle in each issue.
Here’s a relatively easy web crossword puzzle in Japanese.
[QUOTE=Sage Rat]
So far as I am aware, Sudoku was popularised by Americans…
[QUOTE]
The puzzles actually originated in the US, traveled to Japan, got a new name and then came back to the US. Similar puzzles from the Arab world can be traced back to the 13th century.