Packing Parcels

A math puzzle inspired in our daily life. For most children and adults mathematics could be boring and difficult. But everyday we use mathematics to make all sort of things in our life. Packing parcels is one of them.

Everyone already try to tidy up toys in a box or put luggage in the trunk.

To make this puzzle you will need:

• Openscad software (download here)
• A 3D printer or a 3D print service

To solve this puzzle you will need:

• Your brain!
• A printer and Aurasma App (Aurasma) to see the solution

Write the following code in openscad:

difference(){

difference(){

cube([20,20,20], center=true);

cylinder(h=20,r=3, center=true);

}

rotate([90,0,0])cylinder(h=20,r=3, center=true);

rotate([0,90,0])cylinder(h=20,r=3, center=true);

}

On Mac OSX just go to FILE / SAVE

On Mac OSX go to DESIGN / RENDER or hit F6

This is very important, only after you render the object export as stl will be avaiable

On Mac OSX go to FILE / EXPORT / EXPORT AS STL

Write the following code in openscad:

difference(){

difference(){

cube([40,40,20], center=true);

cylinder(h=20,r=3, center=true);

}

rotate([90,0,0])cylinder(h=40,r=3, center=true);

rotate([0,90,0])cylinder(h=40,r=3, center=true);

}

------------

Repeat STEP 3, 4 and 5 to save, render and export the object

Write the following code in openscad:

difference(){

cube([66,66,66], center=true);

translate([0,3,0])cube([63,63,63],center=true);

}

------------
Repeat STEP 3, 4 and 5 to save, render and export the object

Write the following code in openscad:

cube([100,1,3], center=false);

translate([100,0,0])cube([1,3,3],center=false);

------------
Repeat STEP 3, 4 and 5 to save, render and export the object

The stl files to make the puzzle and the trigger for Aurasma:

• Print 3x box1.stl
• Print 6x box2.stl
• Print 1x box3.stl
• Print 1x stick.stl

• Print in photo quality 1x trigger.png

You have to pack all 9 parcels (the green boxes) into the box (red box)

Try to solve it under 15 minutes!

If you put a piece in a wrong place you can use the stick to remove the piece

Using math to solve the problem
Solving this kind of math problems involves geometry. Volume and area are key concepts to complete the task.

Why it's challeging?

The different shapes are not geometrically similar to each other and use different mathematical properties for obtaining their volume or area which is vital for packing objects together.

In this case challenges with cubes are more simple to solve.

Volume box1 = 2x2x2 = 8 cubic centimeters

Volume box2 = 4x4x2 = 32 cubic centimeters

Volume box3 = 6,3x6,3x6,3 = 250 cubic centimeters

Then for solving the problem the 9 parcels have to fit in the volume of the box3

Volume box3 > 3x(Volume box1) + 6x(Volume box2)

250 > 3x8 + 6x32 <=> 250 > 216

It's possible to solve the math problem because the solution is true.

Physics and Chemistry

Atoms and molecules are packed together to form solids, liquids and gases. Particles in a solid are usually more tightly packed together.

And in our daily life

If you use salt to season the food next time remember that all sodium chloride crystal are cube shape.

Inside the crystal sodium ions and chloride ions are packed together.

If you plan a trip and have to pack many things into a small car, you need to use the space efficiently.

If you don’t, you may have to make an extra trip or buy a larger car!

This will be a future project that i made my first steps now. You can use Aurasma to view a augmented reality of this puzzle made by me. You can download the trigger image, print it and use it to see the solution.

I used Blender for animation and Aurasma for Augmented Reality