> My 7 yo pointed out that our 300 piece puzzle actually contains 18 x 18 = 324 pieces and I just don’t know what to believe anymore.

Did they actually count the pieces? In my experience, puzzles are rarely/never simply exact columns and rows of pieces such that you can count the outside edge pieces and multiply to get the number of pieces. Instead there are pieces of all sorts of shapes that create interesting patterns within the puzzle which could result in a number much smaller than multiplying the outside pieces might indicate.