The Puzzler originally operates a business in Metropolis which consists of extorting people if they don't pay him for protection, and in this way eventually crosses paths with Superman. The Puzzler is quite adept at parlor games and puzzles, using both of these in various way to gain the upper hand against Superman.
Once the character is revamped as Valerie Van Haaften, the new Puzzler first appears as an enormous Superman fan, and as a plan to gain his attention joins numerous groups dedicated to super heroes. This idea fails which leads the Puzzler to go down the road of committing crimes, and later accepts a job to assassinate Clark Kent.
The Puzzler was created by Jerry Siegel and John Sikela for use in DC comics, the character first appeared in Action Comics #49 in 1942. The character was eventually revised for the character Valerie Van Haaften who first appeared in Superman Vol. 2, #187 in 2002.
The First Puzzler
In Action Comics #49, the Puzzler was a man who used his amazing cheating skills to win almost any game and was also in the business of blackmail and extortion. He kidnaps Lois Lane many times and forces Superman play for her freedom. The Puzzler always cheats but Superman notices it and was able to turn the tables on him in a game of checkers by using his super-speed to cheat and give the Puzzler a taste of his own medicine. Rather than give up the Puzzler attempts to escape.
The second time he returns in a card game championship as a masked player. Though skillful, he is bested in every game. The Puzzler wants ironic revenge. He is only able to kill one champion, the poker champion. He beat him to death with a fireplace poker. The others (the bridge player who he tries to throw of a bridge; the hearts player to have a heart attack; the rummy champion to die of poisoned rum; the casino player killed in a casino) were saved by Superman. He then followed Puzzler to his hideout and while avoiding his traps, captured the criminal.
The Second Puzzler
Valerie Van Haaften, the second Puzzler first appeared in Superman Vol. 2, #187. She is a huge fan of Superman and in an attempt to get his attention tries joining several superhero organizations. In the end she went for the criminal way. The Puzzler's first task was to kill Clark Kent. She was hired by the Intergang but when she saw Superman she saw an opportunity to get to the top by killing him. She was almost able to defeat Superman until he separated her puzzle pieces, leaving her unable to pull herself back together. Next time she attacked the Secret Six along with many other villains to get the Get out of Hell Free Card. Like the others, she failed.
The New 52
In Justice League of America #3, The Puzzler is seen working for ARGUS. He is male and assumed to be the orginal incarnation. He is working on a slate shingle that dates back to the early 1800's and shards from a stained glass window. He is reassembling them to see what the images mean.
A version of the Puzzler made an appearance in two episodes on the 1960's Batman television series played by Maurice Evans as a potential replacement for the Riddler but the character never made another appearance.
The Puzzler is also mentioned in the movie Batman Forever, as a possible super-villain nickname for the character of Edward Nygma, but ultimately the name "The Riddler" is chosen.
The first Puzzler didn't have any powers, but he was a great cheater and a experienced games-man, especially concerning parlor and board games such as checkers.
The second Puzzler's (Valerie Van Haaften) power consists of little puzzle pieces that are incapable of being destroyed, which she can control, throw, and propel at the same speed as bullets from a gun.