A love jigsaw puzzle is a love letter written on a jigsaw puzzle. The sender is to write a message on a blank puzzle, break it up and send it to a person they love. The receiver then assembles the puzzle to read the message.
In the manga, Sugoroku sold one of these to Hiroto Honda to give to Miho Nosaka. Honda got Yugi to write the letter, and he, Yugi and Katsuya Jonouchi hid it in Miho's desk before class. However, the teacher Ms. Chono found the puzzle during a desk inspection and began solving it herself, reading the message to the class and planned on expelling the sender. However Dark Yugi turned the jigsaw into a Shadow Game, Dark Puzzle, in which Chono felt the pain she was inflicting on others. This caused her makeup to peel away in the shape of jigsaw pieces and reveal her ugly face. Chono then fled the classroom, without announcing or punishing the sender.
In the anime, Sugoroku instead sold the puzzle to Mayumi, who had a crush on Jonouchi. Ms. Chono found it during the inspection, but Mayumi changed her mind about Jonouchi after seeing how he treated the puzzle.