If the USA had some puzzle-cans...Japan surely will as well.
Here is a "Segasonic" branded soda-can-shape puzzle. You slide the tiles around on the surface of the can attempting to put the picture together properly. The pictures here are finger waving Sonic & arms crossed Tails. Because it still has the Segasonic branding, this likely came out right around Sonic 2. This puzzle is uncommon and fetched a fairly high price in Japan when it went to a Japanese auction. Being life-size to a soda can, it's a neat collecible puzzle. discovered by @JapanAnimePosters on Instagram.

In the gallary move puzzle cans can be found. 
Is this 3 entirely different sliding puzzles, or is the photo showing different sides of just 1 or two? Regardless, they all work the same way, sliding tiles around the surface of the soda can shape to assemble the picture properly on all sides of the cylender. These are all based on the same model of a soda can, with textured pull-tab top & curved base. The difference is only in the design printed on it. They are life sized. Due to the open square being visible at the left/bottom of the left can, and right top of the right can it is likely that this is 3 different puzzles, or at the least two. The first has Japanese arms crossed cheerful Tails art. The center has the Sonic/Tails title screen style art, with Segasonic for the banner/ribbon. The right side one has the same cheerful Tails art but adds brown ground, green grass, and hands on hips cheerful Sonic. There also seems to be probably a palm tree in the background. These are not common.