Jigsaw Puzzle Riddle

Number Theory Level 4

John Spilsbury likes jigsaw puzzles and is a mathematics riddler.

He states: "I only own landscape oriented puzzles in which the number of border pieces is exactly \( 8\% \) of the total number of pieces in that puzzle."

From each possible ('landscape' oriented) jigsaw puzzle that can be manufactured according to the given restriction John has one such puzzle in his small collection.

What is the total number of pieces of all of John's puzzles combined?

Note: Corner pieces also belong to the border.


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