xyand the number of circles around the edge is

2x + 2y - 4Since this must be one-half the total number of circles we have

xy = 4x + 4y - 8 xy - 4x - 4y + 16 = 16 - 8 and (x - 4) (y - 4) = 8Since x and y must be integers, so must (x - 4) and (y - 4) and these must be factors of 8. The only integer factors of 8 are (8 and 1) and (4 and 2), which give {x = 12, y = 5} and {x = 8, y = 6}.

Hence the mat must be **12 by 5 circles** or **8 by 6 circles**.

Source: Longley-Cook, L. H.

Categories: Reasoning, Algebra

[Top | Problem]