Blueprint fragments can be acquired at a rate of one per day from the daily quests ,rarely from the Roulette Wheel and sending teams of heroes (2 or more) into the dungeons, or purchased from the store for gems.
Blueprint fragments can be traded for blueprints at the Inn screen.
The innkeeper will offer one chest blueprint from each of the three lines in the table on the right. 
When a blueprint is bought using fragments, the other two offers stay the same, while the next blueprint in the line of the bought one is offered (sorted by level), unless that blueprint was already acquired from a chest, in which case the one after that is offered. As a result, if a player doesn't open any chests and focuses fragments 100% on one line, it will still take probably over a thousand fragments to get to the magic chests recipes that way.