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Problem of the Week
Problem A
3-d Fun

The three-dimensional figure shown was built using interlocking cubes.

The front, the top, and the right side of the figure are visible. The figure has three layers: top, middle and bottom. Each layer has a front row, a centre row and a back row. In the bottom layer, four cubes are visible. These cubes are front left, front right, centre right, and back right. In the middle layer, three cubes are visible. These cubes are front right, centre left and centre right. In the top layer, two cubes are visible. These cubes are centre left and centre right.

When we look at the figure directly from the top, we will see the following image, which is called the top view.

Five identical squares form a shape. The shape looks like a rectangle that is three squares high and two squares wide but is missing the top left square.

  1. How many cubes in total are in the three-dimensional figure? Is there more than one possible answer?

  2. Draw the front view and side view of the figure.