MAΘ Problem Set 5
September 25, 2003
1. Find x if
3
= .3 + .03 + .003 + .0003...
x
2. Let a number be called jagged if every digit differs from those adjacent
to it by an odd number. For instance, 416 is a jagged number because
4 − 1 = 3 and 6 − 1 = 5. How many 3-digit jagged numbers are there?
3. An isosceles trapezoid with bases of 5 and 15 units is covered completely
without overlap or overhang by n congruent triangles. What is the smallest
possible value for n?
4. Three important numbers in mathematics are e, i, and π. Find eiπ given
that eθi = cos θ + i sin θ.
5. A rectangle with one side on the x-axis is inscribed under the graph of
1
. Find the difference between the greatest and least possible values
y = |x|
that the area of this rectangle can take on.
6. Find a fourth-degree polynomialp
with integer coefficients and leading co√
efficient 1, one of whose roots is 2 − 3.