The law of conservation of mass is kind of like that. It says that in any chemical reaction, the total amount of matter you start with (like the pieces of the puzzle) always stays the same, even if it changes form or combines with other things.
Think of it like baking a cake. You start with flour, sugar, eggs, etc. When you bake it, these ingredients change and combine, creating a new cake. But the total weight of all the ingredients in the cake is exactly the same as the total weight of the ingredients you started with. The matter itself just gets rearranged!