Unit Square Shuffle
28 unit squares, when rearranged (and keeping them as whole unit squares), can make three distinct rectangle shapes: 4 by 7, 2 by 14, and 1 by 28. (Rotations are considered identical.)
What's the next largest number divisible by 7 which can also make at least three distinct rectangle shapes?
The answer is 42.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
To find three distinct rectangles we must have at least 6 factors.
Adding 7 we get 35 which has only 4 factors (35, 1, 7, 5)
Adding 7 once more we get 42 which has 8 factors (42, 1, 21, 2, 7, 6, 3, 14)
Therefore 4 2