CMSC150
Introduction to Discrete Math
Spring 2015
Homework 7
February 22, 2015
The total number of points is 15. Your total score will be divided by 15 to produce a
score over 100. Show all work.
1
Prove or disprove.(2 points, 1 point each)
1. The differe
CMSC150
Introduction to Discrete Math
Spring 2015
Homework 4
January 31, 2015
The total number of points is 12. Your total score will be divided by 12 to produce
a score over 100. Show all work. You dont need to compute an exact answer.
Numberonly answer
CMSC150
Introduction to Discrete Math
Spring 2015
Homework 2
January 18, 2015
The total number of points is 10. Your total score will be divided by 10 to produce a
score over 100. Show all work unless checkboxes are provided.
1
For the following binary re
CMSC150
Introduction to Discrete Math
Spring 2015
Homework 5
February 8, 2015
The total number of points is 10. Your total score will be divided by 10 to produce a
score over 100. Show all work.
1
Which of the following are statements? 4 points (1 point e
CMSC150
Introduction to Discrete Math
Spring 2015
Homework 6
February 15, 2015
The total number of points is 10. Your total score will be divided by 10 to produce a
score over 100. Show all work unless checkboxes are provided.
1
Using the predicate symbol
CMSC150
Introduction to Discrete Math
Spring 2015
Homework 3
December 28, 2014
The total number of points is 10. Your total score will be divided by 10 to produce a
score over 100. Show all work unless checkboxes are provided.
1
Decide whether each of the
CMSC150
Introduction to Discrete Math
Spring 2015
Homework 1
January 3, 2015
The total number of points is 10. Your total score will be divided by 10 to produce a
score over 100. Show all work.
1
Describe the following set by listing its elements:(1 point
Stable Marriage and ManOptimality
Definition 1. A man m and a woman w are valid partners means there exists
a stable matching in which they are paired with each other.
Definition 2. For every man m, ms best valid partner (denoted best(m)
is the highestr
[Illustration]
In introducing a little Commonwealth problem, I must first explain that
the diagram represents the sixtyfour fields, all properly fenced off
from one another, of an Australian settlement, though I need hardly say
that our kith and kin "dow
[Illustration:
(1)
(2)
(2)
(4) (5) (1) (6) (7)
(3) (4) (9) (5) (6)
(3)
(7)
A
(8)
(8)
B
(9)
]
278.A DORMITORY PUZZLE.
In a certain convent there were eight large dormitories on one floor,
approached by a spiral staircase in the centre, as shown in our pla
ground on which he decided to build eight villas, as shown in the
illustration, with a common recreation ground in the middle. After the
houses were completed, and all or some of them let, he discovered that
the number of occupants in the three houses for
335.FARMER LAWRENCE'S CORNFIELDS.
One of the most beautiful districts within easy distance of London for a
summer ramble is that part of Buckinghamshire known as the Valley of the
Chessat least, it was a few years ago, before it was discovered by the
sp
you change the direction of your pencil it begins a new stroke. You may
go over the same line more than once if you like. It requires just a
little care, or you may find yourself beaten by one stroke.
[Illustration]
242.THE TUBE INSPECTOR'S PUZZLE.
The m
Now, in order to reduce their growing obesity, and to combine physical
exercise with mental recreation, the prisoners decided, on the
suggestion of one of their number who was interested in knight's tours,
to try to form themselves into a perfect knight's
without mutual attack. I shall give an exceedingly simple rule for
determining the number of ways for a square chequered board of any
number of squares.
300.THE EIGHT QUEENS.
[Illustration:
+++++++++
    .Q    
++++.+++++
  .Q. 
245.THE FLY ON THE OCTAHEDRON.
"Look here," said the professor to his colleague, "I have been watching
that fly on the octahedron, and it confines its walks entirely to the
edges. What can be its reason for avoiding the sides?"
"Perhaps it is trying to s
263.KING ARTHUR'S KNIGHTS.
King Arthur sat at the Round Table on three successive evenings with his
knightsBeleobus, Caradoc, Driam, Eric, Floll, and Galahadbut on no
occasion did any person have as his neighbour one who had before sat
next to him. On
There are no morals in puzzles. When we are solving the old puzzle of
the captain who, having to throw half his crew overboard in a storm,
arranged to draw lots, but so placed the men that only the Turks were
sacrificed, and all the Christians left on boa
once. How would you arrange them?
If we represent them by the first nine letters of the alphabet, they
might be grouped on the first day as follows:A B C
D E F
G H I
Then A can never walk again side by side with B, or B with C, or D with
E, and so on. Bu
+++++++++
  EVLI  
+++++++++
  LIEV  
+++++++++
]
If the reader will examine the above diagram, he will see that I have so
placed eight V's, eight E's, eight I's, and eight L's in the diagram
that no letter is in
297.BISHOPSUNGUARDED.
Place as few bishops as possible on an ordinary chessboard so that every
square of the board shall be either occupied or attacked. It will be
seen that the rook has more scope than the bishop: for wherever you
place the former, it
Once upon a time the Lord Abbot of St. Edmondsbury, in consequence of
"devotions too strong for his head," fell sick and was unable to leave
his bed. As he lay awake, tossing his head restlessly from side to side,
the attentive monks noticed that somethin
same. Only remember this: that in no case may two of you ever be
together in the same cell."
One of the prisoners, after working at the problem for two or three
days, with a piece of chalk, undertook to obtain the liberty of himself
and his fellowprisone
NONATTACKING CHESSBOARD ARRANGEMENTS.
We know that n queens may always be placed on a square board of n squared
squares (if n be greater than 3) without any queen attacking another
queen. But no general formula for enumerating the number of different
way
that this arrangement will not answer the conditions, for in the two
directions indicated by the dotted lines there are three queens in a
straight line. There is only one of the twelve fundamental ways that
will solve the puzzle. Can you find it?
301.THE
you arrange them? It will be found that of the twelve shown in the
diagram only four are thus protected by being a knight's move from
another knight.
THE GUARDED CHESSBOARD.
On an ordinary chessboard, 8 by 8, every square can be guardedthat is,
either oc
  * * 
+++++++
 *
+++

+++
In the illustration we have a somewhat curious target designed by an
eccentric sharpshooter. His idea was that in order to score you must hit
four circles in as many shots so that those four shots shall form
not enter.
Well, the captain says that if a spirited lion crosses your path in the
desert it becomes lively, for the lion has generally been looking for
the man just as much as the man has sought the king of the forest. And
yet when they meet they always
last cigar, assuming that they each will play in the best possible
manner? The size of the table top and the size of the cigar are not
given, but in order to exclude the ridiculous answer that the table
might be so diminutive as only to take one cigar, we