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GCSE Maths - Cargo Project

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Boxes are waiting on the quayside to be loaded onto a ship. 27 boxes are made up into a 3 x 3 x 3 cube ready for the crane. The dockers stick labels as shown on each of the 6 exposed faces of the cube. The cube is dropped as it is being loaded and the boxes are scattered. My mission is to find how many labels have 3, 2, 1 and no labels. I should also try to find a formula for any cube size, for how to work out how many 3, 2, 1 and no labels they have.

I have decided to draw out my cubes first. I will have a different colour to represent each label amount, e.g. blue for 3 labels, red for 2, etc.

...read more.


 level – Birds Eye View


3 labels


2 labels


1 label

No labels



1st level – Birds Eye View2nd level – Birds Eye View


3rd level – Birds Eye View4th level – Birds Eye Viewimage14.pngimage13.png


3 labels

2 labels


1 label

No labels




...read more.


The formula for no labels is


The no labeled boxes are in the centre of the cube and cannot be spotted by looking at the outside of the box. You have to use minus 2 to show that the corners are not included and then cubed because it is the inside.

After looking carefully at my results I have found formulas for how to work out any amount of labels. I have tested these formulas on a 6 by 6 by 6 square. They worked. The edges, corners and faces a cube affected these formulas. Maybe next time I will try to work why this is.

...read more.

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