All the pieces should fit in the big box.
A large paper box filled with smaller rectangular and cubic paper boxes.
If you slice off all the cubes on the left hand side, you’ll find another square of nine cubes. This means you’ll need a small present on the left hand side, one on the right hand side, and one in the middle. You also need one on the front face, and one on the back face, and one in the middle. If you put the three little cubes on a diagonal going from top front left to bottom back right, then you should be able to fit the other presents around them.
Real-life maths
This sort of puzzle is called a packing problem. Other examples of packing problems include trying to fit bags into a car when you go on holidays, or trying to get all your stuff into a cupboard when you are tidying your room. A good strategy for these sorts of problems is to make big, closely packed groups of things, and then try to fit all those groups into the container. This will often give you a good packing, but it won’t necessarily give you the best packing. In this puzzle, making a big block out of three big presents won’t lead to the correct solution.