Oranges are placed in a pyramid-like stack with each layer completely filled. The base is a rectangle that is 5 oranges wide and 7 oranges long. Each orange, above the first layer, rests in a pocket formed by four oranges in the layer below, as shown. The last layer is a single row of oranges. The total number of oranges in the stack is
Because of the way in which the oranges are stacked, each layer is a rectangle whose length is 1 orange less and whose width is 1 orange less than the layer below.
The bottom layer is 5 by 7 and so contains 35 oranges.
The next layer is 4 by 6 and so contains 24 oranges.
The next layer is 3 by 5 and so contains 15 oranges.
The next layer is 2 by 4 and so contains 8 oranges.
The next layer is 1 by 3 and so contains 3 oranges. This is the last layer, as it consists of a single row of oranges.
The total number of oranges in the stack is thus .