The National Diet Library's mini-page about the Japanese Calendar has a delightful section called Unriddling the Daisho-reki calendar.

According to the lunisolar calendar, there were long months with 30 days and short ones with 29 and their arrangement changed year by year. So knowing the arrangement of long and short months, with the inclusion of an intercalary month from time to time, was very important for the people who lived in those times. Merchants, who made it a rule to effect payments or collections at the end of each month, would make signs to show a long or short month and erect them up in their shops according to the month in order to avoid mistakes. ...
The Daisho-reki calendar, which showed only the order of the long and short months, appeared during the Edo period (1603-1867). In those days it was called simply "Daisho." But instead of merely showing the length of month, it incorporated such devices as indicating long and short months with the use of pictures and sentences. ...
Later, in the Meiji era, when the solar calendar was officially adopted, Daisho calendars fell into disuse and were no longer produced. However, the puzzles they included continue to excite interest even today. From generations people have collected Daisho calendars and many of them are kept in the National Diet Library. So let us try to solve a few of their puzzles.

Yes, let's! The page includes all the information about characters and things you need to know to solve the puzzles, even if you don't read any Japanese at all.

The gallery elsewhere on the site has a few other interesting sections, too. Sadly, the most exciting part (for me) is in Japanese only: Rare Books!

Here's the list of what they have, or you can start from Book Number 001 (the Āryasarvapuṇyasamuccayasamādhi Sutra, if memory serves*) and just keep clicking on 次 to go forward.

Most of them are just scans of the cover or first page or two, as far as I can tell, but there are exceptions. Look for and click on the phrase "特別展示があります" below the photos, and be rewarded with a peek inside, among other things:

• 『青楼美人合』 ("Collection of young-sakura [i.e. Yoshiwara] beauties")
• 『江戸近郊八景之内』 ("Eight views on the outskirts of Edo")
• 『潮干のつと』 ("Clam-digging souvenir")
• 『彩色美津朝』 ("Color [book of the] New Year")

Also, this isn't a complete work, but I just had to share it: a scene from the completely unacceptable tale Nansou Satomi Hakkenden, in which (spoilers) the deceased Fusehime and her dog-husband Yatsufusa return from the dead long enough to shoot some sort of ray at a scoundrel or two. Or maybe it's a printing error? I have to admit I'm not that familiar with the story, because ew.

And finally, just so that this blog doesn't degenerate into a collection of links to scans of old books, let's talk about 美津朝 as a word for "new year". Pronounced mitsu no asa, it means "three mornings". (美津 are ateji for 三つ, and the no is not actually written, as was very common in the Olden Days.) The "three mornings" are, of course, the dawn of the new year, the dawn of the first month in that year, and the dawn of the first day in that month. Cool, huh? Also expressible as sanchou, 三朝, which was probably borrowed along with the calendar from China.

* Okay, okay, I googled it.