Developer Andrey Yefimov has some sample source code up for building a Fifteen puzzle with Delphi XE6 Firemonkey. In his blog post he explains that the game ‘Tag’ was invented in 1878 by Noah Chapman. He created the game using TRectangle’s for the pieces and TFloatAnimation to slide them around. The game basically has a grid of 15 tiles (one space is missing which makes the 16th space in a 4×4 grid). The goal of the game is to get the numbers in order with the least amount of moves. There is an explanation near the end of the blog post where he explains what the variables are that he used to create the project. The game was designed for Android but I don’t see any reason it won’t run on all supported platforms like Windows and IOS. There is a video at the end of the blog post which demonstrates how the game works. The blog post is in Russian I believe so be sure to use Chrome and auto translate it to your language.
Or here is a mirror of the Tag game source code.