A puzzle was a type of game played by species such as Humans. One type was the jigsaw puzzle that involved putting irregular shaped pieces together to create a picture.
In 2364, Lieutenant Commander Data and Lieutenant Geordi La Forge both got their fingers stuck in a Chinese finger puzzle. (TNG: "The Last Outpost")
In 2368, Clara Sutter put together a puzzle in her bedroom. She asked Isabella for help, but Isabella wanted to sneak away with her to visit Engineering. (TNG: "Imaginary Friend")
In 2369, Lieutenant Jadzia Dax compared the Altonian brain teaser to a puzzle. (DS9: "A Man Alone")
In 2370, several characters on the holodeck of the USS Enterprise-D put together a puzzle while on the Orient Express. (TNG: "Emergence")
Benjamin Sisko referred to the lost Bajoran city of B'hala as an "ancient puzzle" in 2373. (DS9: "Rapture")
In 2377, Icheb and Naomi Wildman put together a puzzle depicting DNA together in one of the USS Voyager's cargo bays. (VOY: "Shattered")