Open Middle®
Directions: Using the digits 1 to 9, at most two times each, place a digit in each box to make two circles: one with an area of less than 10 units2 and one with more than 10 units2.
Hint
How do we ensure that the digits we choose create a circle? How do the digits we choose affect the size of our circle?
Answer
There are many possible answers but all must have the coefficients of x and y equal to the same value. One example is:
2x2 + 2y2 = 9 for an area of ~14.13 units2 and 5x2 + 5y2 = 4 for an area of ~14.13 units2
2x2 + 2y2 = 9 for an area of ~14.13 units2 and 5x2 + 5y2 = 4 for an area of ~14.13 units2
Source: Robert Kaplinsky