Some "15" puzzles are unsolvable

The example shown, posted on the puzzles subreddit, is on a watch.  What I remember are the old "analog" versions with small sliding wooden pieces in a frame.  I used to get great satisfaction as a child by solving scrambled puzzles.  What I learned this morning is that the puzzles date back way before my time:

The puzzle was "invented" by Noyes Palmer Chapman, a postmaster in Canastota, New York, who is said to have shown friends, as early as 1874, a precursor puzzle consisting of 16 numbered blocks that were to be put together in rows of four, each summing to 34 (see magic square)... The game became a craze in the U.S. in 1880...

Some later interest was fueled by [Sam] Loyd's offer of a $1,000 prize (equivalent to $34,996 in 2024) to anyone who could provide a solution for achieving a particular combination specified by Loyd, namely reversing the 14 and 15, which Loyd called the 14-15 puzzle. This is impossible, as had been shown over a decade earlier by Johnson & Story (1879), because it requires a transformation from an even to an odd permutation.

The Reddit thread confirms that the one illustrated is unsolvable, which is confirmed at the Wikipedia entry.  In fact, half of all initial states of the puzzle will be mathematically impossible to resolve.  To guarantee solvability, a puzzle would need to be manufactured with the pieces "solved" and then scrambled before distribution (or by asking the end-user to do so).  I'm glad all my childhood versions were solvable.