Mathematics Magazine for Grades 1-12
We need a moral philosophy in which the concept of love, so rarely
mentioned now by philosophers, can once again be made central.
Three cubes, whose edges are 2, 6, and 8 centimeters long, are glued together at their faces. Compute the minimum surface area possible for the resulting figure.
536 square centimeters.
Before gluing, the total surface area is 6(4 + 36 + 64) = 6(104), or 624, square centimeters. The minimum surface area is achieved if each cube is glued to both others, as shown. Twice the surface area of one face of the smaller cube is removed in each gluing. Therefore, we must subtract 2(4 + 4 + 36), or 88, square centimeters from 624 square centimeters to get 536 square centimeters.
Determine the values of the three different digits d, a, and n given the following:
d = 4, a = 9, and n = 5.
Looking at the tens-digit sum, we see that a is either 0 or 9, depending on whether a + n is smaller than 10 in the ones place. However, if a = 0, then n = d according to the ones-place sum.
Since we know that a, d, and n are unequal, we see that a = 9 and a + n is at least 10, as is n + a + 1, "carrying" from the ones place to the tens place. We therefore conclude that d + d + 1 = a = 9, so d = 4. Finally, we see that n = 5, giving us
The point (a, b) is reflected over the y-axis to the point (c, d), which is reflected over the x-axis to the point (e, f). Compute ab - ef.
When the point (a, b) is reflected about the y-axis, it "lands" at the point (-a, b); and when that point is reflected about the x-axis, it lands on (-a, -b). Therefore, e = -a and f = -b, so ab - ef = ab - ab = 0.
Simplify the following , where x ≥ 0 and y ≥ 0