trait for a total of 8. Since each woman
sion as n approaches infinity; when i
is 1, this limit is defined as e, the base
Perfect *Beaudet, Paul R.
ra, three traits; A also cannot be rb and
rr, for then she would also be ra, three
answer is approaching e times 108.
traits. Therefore, A is ra, rb or ra, rr,
4 The distance of the center of the 1-
Barb (B) and Cleo (C) are ri, rr, and one
four traits; and A cannot be ra, rr, for
possibilities for this: (1) ra, rb, ri; (2)
ra, rb, rr; (3) ra, ri, rr; and (4) rb, ri, rr.
4√3. AC = √(62 -22) = 4√2, and BC =
√(52 -12) = 2√6. Let d be the center
four traits; (3) can be eliminated since
AD = √{52 – (H – 4)2}, BD = √{42 – (H
– 3)2} , and CD = √{32 – (H – 2)2}. Use
also ra, which leaves rb for B, but then
B is also ra, so all three are ra. Thus,
C must be ra, rb, ri, and B is ri, rr; so
2 An estimated 18.37 percent of the
Yes,” “Answer No,” and “Have You
5 The young girl should release from
Cheated” cards are selected with equal
static position. She will land about 8.7
is 784 for each card. Then 928 – 784 =
lum, which the swing is, total energy is
difficult regular problem was No. 5 about
mg(h – h ), plus kinetic energy, mv2/2,
the vertical belt sander. However, of the
at any point in its arc. Equating kinetic
and potential energy gives v2/2 = gh
– gh, so v = √[2g(h – h)] = √[2gL(cosθ
3 After one year, you will owe the
cal and L is the length of the chains.
Reader’s entries for the Fall problems will
is (1 + i/n)n, where i is the annual inter-
trajectory of a projectile, which are x 1 Cleo is not remarkably rich. There
est rate and n is the number of times
= x + v t and 0 = y + v t – gt2/2. Now, v
are four “remarkable” traits—artistic
= vcosθ and v = vsinθ. Solving for t (the
(ra), beautiful (rb), intelligent (ri), and
time it takes the girl to hit the ground)
gives t = [v + √(v 2 +2gy )]/g. Substi-
tuting into the equation for x gives x
= x + (vcosθ/g)[(vsinθ + √(v2sin2θ +
2gy )], where x = Lsinθ and y = L(1
1 Find the smallest positive integer
– cosθ) + h . Using trial and error (with
L = 6 ft and h = 2 ft) on the swing’s
5 A sparrow, flying horizontally in a
straight line, is 20 m directly below an
B onus. The punter should aim at the —Christopher R. Oliver, AL E ’08 2 Five pirates find a chest contain-
tion is given by p = [1/(σ√(2π))]exp(-
θ2/2σ2), where θ is the deviation from
hawk is flying at 30 m/s, how fast is the
the aim angle, θ and varies from -45o to
+45o, and σ = 7.5 is the standard devia-
vote, and if half or more of the pirates
B onus. A regular dodecahedron has
After all, this is football!) Pick a yard-
line aim point y ; then the aim angle
gons. If some, including none or all, of
is given by θ = tan-1[(50-y )/(80/3)].
by y = 50-(80/3)tan(θ +θ), except that
when y is negative (indicating that the
ball crossed the goal line), y = 20. The
expected value of the yard line for spot-
-45o to +45o of pydθ. It is easy to write a
C omputer Bonus. A, B, and C are
program that varies y to find the mini-
3 My wife and I recently attended a
use the digits 1 through 9 once and only
fies the equation, A x B = C2, and where
well. Program the expressions for y
and p into the spreadsheet (with y
as a variable), and calculate y for unit
increases in θ from -45 to 45. (This is
sufficiently accurate for this problem.)
with various values of y until the mini-
Tau Beta Pi, P. O. Box 2697, Knoxville, TN 37901-2697 or email to BrainTick- [email protected] only as plain text. The
C omputer Bonus. The next two pal-
with 16 digits! This is quite a distance
4 Professor Asterisk treated his
to the judges who are Dr. H.G. McIl- abcddcba where a can equal 1, 4, 5, 6,
vried III,PA G ’53;F. J. Tydeman,CA
or 9 and b, c, and d can equal 0 through
Δ ’73;J. L. Bradshaw,PA A ’82; and the —D. A. Dechman,TX A ’57.
6, 8, 10, 12, 14, and, finally, 16-digit
in the range of 29 to 39, inclusive. After

IN THE UNITED STATES DISTRICT COURT FOR THE EASTERN DISTRICT OF PENNSYLVANIA IN RE FASTENERS ANTITRUST MDL Docket No. 1912 LITIGATION : ___________________________________ : THIS DOCUMENT RELATES TO: ____________________________________: MEMORANDUM OF LAW IN SUPPORT OF CO-LEAD COUNSEL’S JOINT PETITION FOR AWARD OF COUNSEL FEES, PAYMENT OF COSTS AND EXPENSE

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