ENGR. BESAVILLA’S NOTES
Problem 17 Problem 24
A jig-saw puzzle contains 100 pieces. A “move” consists of nonnecting two The following pairs are members of a certain relation: (Sacramento, Carson
clusters (including “clusters” of just one piece.) What is the minimum number City), (Pierre, Bismark), (Juneau, Olympia), and (Albany, Hartford).
of moves required to complete the puzzle? Moreover, the reversals of the first two pairs are also members, while those
of the latter two are not. What is the relation?
Ans: 99
Ans: (x,y) is a member only if y is the nearest state capital to
state capital x.
Problem 18
A novice librarian shelved a twelve volume set of encyclopedias in the
following order from left to right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and Problem 25
2. Using her system, where will the annual supplement, Volume 13, go? Four players played a hand of hearts at $1 a point (pairwise payoffs). Dave
lost $10 to Arch, $12 to Bob, and $20 to Chuck. How many hearts did poor
Ans: Between 10 and 3 Dave take in?
Ans: 4
Problem 19
“Four” in English, “cinco” in Spanish, and “ni” and “san” in Japanese share an
interesting property. What is it? Problem 26
In a memorable game with the Podunk Polecats, the Mudville Mets
Ans: Each of these numbers is equal to the number of letters in established a record. They received the maximum number of walks possible
in one inning in which one player (who happened to ne the Mighty Casey)
its name
was up three times and accounted for all three outs. How many walks did
Podunk allow in that tedious half-inning?
Problem 20 Ans: 30
The League Against Restrictive Diets, with members all over the U.S. plans a
convention. Most of the members live in Chicago, so they feel that city is the
logical site. The other members suggest some city representing the Problem 27
“weighted centroid” of the League. If the object is to minimize total distance Mary Ann Moore’s father has a yacht and so has each of his four friends:
traveled by the members of the L.A.R.D. who is right? Colonel Downing, Mr. Hall, sir Barnacle Hood, and Dr. Parker. Each of the
five also has one daughter and each has named his yacht after a daughter of
Ans: Chicago is the proper site.
one of the others. Sir Barnacle’s yacht is the Gabrielle, Mr. Moore owns the
Lorna; Mr. Hall the Rosalind. The Melissa, owned by Colonel Downing, is
named after Sir Barnacle’s daughter. Gabrielle’s father owns the yacht which
Problem 21
is named after Dr. Parker’s daughter. Who is Lorna’s father?
In Greenwich Village, tic-tac-toe is played in an unusual way. At each turn a
player marks as many squares as he wishes provided they are in the same Ans: Colonel Downing
vertical or horizontal row(they need not be adjacent). The winner is the one
who marks the last square. Which player has the advantage and what
strategy should he employ? Problem 28
A Solid State Physicist gives a small stag party. He invites his father’s
Ans: 2nd player brother-in-law, his brother’s father-in-law, his father-in-law’s brother, and his
The 2nd marks two to form a connected right angle and brother-in-laws father. Find the number of guests.
marks as many as necessary to complete either an L or a T
of 5 squares. Ans: two including the host
Problem 22 Problem 29
With some sharp reasoning, you ought to be able to determine the last Assume that every tree has at least one leaf, If there are more trees than
member of the sequence for which the first 20 members are: 11, 31, 71, 91, there are leaves on any one tree, then there exist at least two trees with the
32, 92, 13, 73, 14, 34, 74, 35, 95, 16, 76, 17, 37, 97, 38, 98, _____? same number of leaves. Is the conclusion valid?
Ans: Its valid
Ans: 79
Problem 30
Problem 23
A rich farmer had 15 children by first wife 15 by his second. The second wife
A simple substitution cipher message was worked out on a black-board and
wished to insure the heritage to one of her own children and persuaded him
accidentally erased. A few fragments remain, however. The word G Q K X Y
to seat all 30 in a circle and count off every tength child until 1 remained. The
J has escaped erasure with X identified as R and Y as B. Also the word P K
first 14 thus eliminated were all his first wife’s children. From this point on he
Z X D V can be made out with Z identified as L. The only other legible word
insisted that they count backward from his first wife’s lone remaining child. In
is K V J Z D C. What word does this represent?
what order were his first wife’s children? Who became heir?
Ans: ASYLU Ans: 2nd wife
Problem 17 Problem 24
A jig-saw puzzle contains 100 pieces. A “move” consists of nonnecting two The following pairs are members of a certain relation: (Sacramento, Carson
clusters (including “clusters” of just one piece.) What is the minimum number City), (Pierre, Bismark), (Juneau, Olympia), and (Albany, Hartford).
of moves required to complete the puzzle? Moreover, the reversals of the first two pairs are also members, while those
of the latter two are not. What is the relation?
Ans: 99
Ans: (x,y) is a member only if y is the nearest state capital to
state capital x.
Problem 18
A novice librarian shelved a twelve volume set of encyclopedias in the
following order from left to right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and Problem 25
2. Using her system, where will the annual supplement, Volume 13, go? Four players played a hand of hearts at $1 a point (pairwise payoffs). Dave
lost $10 to Arch, $12 to Bob, and $20 to Chuck. How many hearts did poor
Ans: Between 10 and 3 Dave take in?
Ans: 4
Problem 19
“Four” in English, “cinco” in Spanish, and “ni” and “san” in Japanese share an
interesting property. What is it? Problem 26
In a memorable game with the Podunk Polecats, the Mudville Mets
Ans: Each of these numbers is equal to the number of letters in established a record. They received the maximum number of walks possible
in one inning in which one player (who happened to ne the Mighty Casey)
its name
was up three times and accounted for all three outs. How many walks did
Podunk allow in that tedious half-inning?
Problem 20 Ans: 30
The League Against Restrictive Diets, with members all over the U.S. plans a
convention. Most of the members live in Chicago, so they feel that city is the
logical site. The other members suggest some city representing the Problem 27
“weighted centroid” of the League. If the object is to minimize total distance Mary Ann Moore’s father has a yacht and so has each of his four friends:
traveled by the members of the L.A.R.D. who is right? Colonel Downing, Mr. Hall, sir Barnacle Hood, and Dr. Parker. Each of the
five also has one daughter and each has named his yacht after a daughter of
Ans: Chicago is the proper site.
one of the others. Sir Barnacle’s yacht is the Gabrielle, Mr. Moore owns the
Lorna; Mr. Hall the Rosalind. The Melissa, owned by Colonel Downing, is
named after Sir Barnacle’s daughter. Gabrielle’s father owns the yacht which
Problem 21
is named after Dr. Parker’s daughter. Who is Lorna’s father?
In Greenwich Village, tic-tac-toe is played in an unusual way. At each turn a
player marks as many squares as he wishes provided they are in the same Ans: Colonel Downing
vertical or horizontal row(they need not be adjacent). The winner is the one
who marks the last square. Which player has the advantage and what
strategy should he employ? Problem 28
A Solid State Physicist gives a small stag party. He invites his father’s
Ans: 2nd player brother-in-law, his brother’s father-in-law, his father-in-law’s brother, and his
The 2nd marks two to form a connected right angle and brother-in-laws father. Find the number of guests.
marks as many as necessary to complete either an L or a T
of 5 squares. Ans: two including the host
Problem 22 Problem 29
With some sharp reasoning, you ought to be able to determine the last Assume that every tree has at least one leaf, If there are more trees than
member of the sequence for which the first 20 members are: 11, 31, 71, 91, there are leaves on any one tree, then there exist at least two trees with the
32, 92, 13, 73, 14, 34, 74, 35, 95, 16, 76, 17, 37, 97, 38, 98, _____? same number of leaves. Is the conclusion valid?
Ans: Its valid
Ans: 79
Problem 30
Problem 23
A rich farmer had 15 children by first wife 15 by his second. The second wife
A simple substitution cipher message was worked out on a black-board and
wished to insure the heritage to one of her own children and persuaded him
accidentally erased. A few fragments remain, however. The word G Q K X Y
to seat all 30 in a circle and count off every tength child until 1 remained. The
J has escaped erasure with X identified as R and Y as B. Also the word P K
first 14 thus eliminated were all his first wife’s children. From this point on he
Z X D V can be made out with Z identified as L. The only other legible word
insisted that they count backward from his first wife’s lone remaining child. In
is K V J Z D C. What word does this represent?
what order were his first wife’s children? Who became heir?
Ans: ASYLU Ans: 2nd wife
