Potentials - January/February 2017 - 48
gamesman problems
by Vaughan Clarkson
Problem #1: lightbulb Moment
Problem #3
Given an m # n matrix A and an n # m
matrix B, prove that tr (AB) = tr (BA) ,
where tr ($) represents the trace of
the matrix.
You have three identical incandescent
light globes such as you might use
to ambush electrical engineering
graduands (https://youtu.be/
aIhk9eKOLzQ). You connect
two in parallel and the third in
series with the first two. You
then apply an appropriate
power source. Is any globe
brighter than any other? If so,
by how much?
Problem #4
If A, B are n # m matrices,
then AB - BA cannot be a
nonzero multiple of the id-
ent it y. (AB - BA is t he Lie
bracket of A and B.)
Problem #2: Cost of Equilibrium
Problem #5
p
Numbers-© CaN stoCk Photo/agsaNdrew,
There are two identical ideal capacitors
Show that if p is prime, then a k k,
aNdroid-© CaN stoCk Photo/kirstyPargeter
0 1 k 1 p, is divisible by p.
connected by an ideal switch. One
capacitor is charged to voltage V0 . The
acknowledgments
other is uncharged. You close the switch and allow the
Problems #1 and #2 were supplied by Peter Farrell and
system to come to equilibrium. Initially the energy in the
Problems #4 and #5 were suggested by Bill Moran, both
system is CV 20 /2. Later, the voltage on each capacitor is
V0 /2 , and the stored energy is C (V0 /2) 2 = CV 20 /4 . Where
of Melbourne, Australia.
did the energy go?
Here are some problems in mathematics. Can you prove
each one in 100 characters or fewer? (You don't need to
count spaces within equations.)
Digital Object Identifier 10.1109/MPOT.2016.2617404
Date of publication: 10 January 2017
If you have a problem for the Gamesman,
submit it along with the solution
to potentials@ieee.org. If we publish your problem,
you'll receive a free IEEE t-shirt, so please
include your size. thanks.
solutions are on page 5.
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January/February 2017
IEEE PotEntIals
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Problems #3-5: 100-Character Challenges
https://www.youtu.be/
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Table of Contents for the Digital Edition of Potentials - January/February 2017
Potentials - January/February 2017 - Cover1
Potentials - January/February 2017 - Cover2
Potentials - January/February 2017 - 1
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Potentials - January/February 2017 - 3
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Potentials - January/February 2017 - 45
Potentials - January/February 2017 - 46
Potentials - January/February 2017 - 47
Potentials - January/February 2017 - 48
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