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## Tbp.org

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,

*mv*2/2,
the vertical belt sander. However, of the
at any point in its arc. Equating kinetic
and potential energy gives

*v*2/2 = g

*h *
– g

*h*, so

* v* = √[2g(

*h * –

*h*)] = √[2g

*L*(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* – g

*t*2/2. Now,

*v *
are four “remarkable” traits—artistic
=

*v*cosθ and

*v * =

*v*sinθ. Solving for

*t* (the
(ra), beautiful (rb), intelligent (ri), and
time it takes the girl to hit the ground)
gives

*t* = [

*v * + √(

*v *2 +2g

*y *)]/g. Substi-
tuting into the equation for

*x* gives

*x*
=

*x * + (

*v*cosθ/g)[(

*v*sinθ + √(

*v*2sin2θ +
2g

*y *)], where

*x * =

*L*sinθ 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(-
θ

*2*/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

*py*dθ. 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-*
*lers@tbp.org* 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

Source: http://www.tbp.org/pubs/BTs/W11.pdf

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