Potentials - May/June 2017 - 5

gamesman solutions

by Athanasios Kakarountas

solution #1: swap Meet

Considering that the probability of get-
ting any number between one and six
is basically a one out of two proba-
l
A = A + B //A = A + B
bility of getting a zero on the paint-
B = A - B //Bl = A l - B = A + B - B = A
ed die, and one out of six on the
A = A - B //A m = A l - Bl = A + B - A = B.
normal die, it turns that it actu-
There is a restriction regarding the
ally is one out of 12. The same
result of the arithmetic functions.
is true for a number from seven
The selection of the wrong data type
to 12.
may result in overflow and, conse-
So you have a one out of 12
quently, erroneous results.
chance of getting any number from
one to 12.
solution #2: Doggin' It!
NOTE: A one-out-of-six chance
This is a problem that was asked to
is achievable if the blank die was left
John von Neumann, who was known
blank or painted with only one num-
Numbers-© CAN stoCK Photo/123dArtist,
ANdroid-© CAN stoCK Photo/KirstyPArgeter
for solving difficult problems as well as
ber. However, if we choose to paint
his speed in doing so. He replied in just
the blank die with three numbers,
3 s that the answer is 20 km. Although most people
then there are at least two pairs with a higher pos-
try to approach the solution as a series of repeated
sibility to appear.
steps, it is much simpler. Since the man has a steady
solution #5: squared away
pace of 4 km/h, he needs 2 h to reach his house door.
Considering that the dog has a steady velocity of
10 km/h no matter the direction, then, in 2 h, the dog
ran 20 km.
We can use mathematic attributes. So

solution #3: thinking Inside the Box
Eleven cartons total.
Seven large boxes (7 * 8 = 56 boxes).
Four small boxes (4 * 10 = 40 boxes).
Eleven total cartons and 96 boxes.

solution #4: a Dicey situation
If the two dice were normal, then it is easy to find that
some numbers correspond to more combinations, so
there's a higher chance for them to appear. The goal is to
equalize the possibility of a number's appearance.
The approach is reducing the total number of pos-
sible combinations. Painting the second die with three
zeroes (no dots) and three sixes, you have a one out of two
chance of getting either a zero or a six. With this trick,
the numbers that can appear are one to 12 (zero to the
altered dice plus the number on the normal dice or six
plus the number on the normal dice).

Digital Object Identifier 10.1109/MPOT.2017.2668780
Date of publication: 8 May 2017

IEEE PotEntIals

May/June 2017

■

5



Table of Contents for the Digital Edition of Potentials - May/June 2017

Potentials - May/June 2017 - Cover1
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Potentials - May/June 2017 - 1
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Potentials - May/June 2017 - Cover3
Potentials - May/June 2017 - Cover4
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