CHAPTER 2 Flashcards
LORNA’S FATHER
Mary Ann Moore’s father has a yacht and so has each of his four friends: 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 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 is named after Dr. Parker’s daughter. Who is Lorna’s father?
- Lorna - Colonel Downing
Gabrielle - Mr. Hall
Melissa - Sir Barnacle Hood
Rosalind - Dr. Parker
Mary Ann - Moore
NUMBER GUESTS, FATHER’S BROTHER IN LAW
A Solid State Physicist gives a small stag party. He invites his father’s brother-in-law, his brother’s father-inlaw, his father-inlaw’s brother, and his brother-in-law’s father. Find the number of guests
- A party of 2, including the host
TREE WITH AT LEAST ONE LEAF
Assume that every tree has at least one leaf. If there are more trees than there are leaves on any one tree, then there exist at least two trees with the same number of leaves. Is the conclusion valid?
- it’s valid
If the conclusion were not valid, then every tree would have a different number of leaves; and you’d run out of leaves before you ran out of trees.
RICH FARMER 15-15 CHILDREN
A rich farmer had 15 children by his first wife and 15 by his second. The second wife wished to insure the heritage to one of her own children and persuaded him to seat all 30 in a circle and count off every tenth child until only 1 remained. The first 14 thus eliminated were all his first wife’s children. From this point on he insisted that they count backward from his first wife’s lone remaining child. In what order were his first wife’s children? Who became heir?
16th (he knew 16 would survive 15 eliminations)
2nd wife knew the first 14 eliminations would occur at positions 3, 7 ,8 ,9 ,10, 11, 15, 20, 22, 23, 24, 26, 27, and 30.
MR. BROWN, MR. GREEN, MR. WHITE, MR. BLACK
A college president, a professor, an instructor, and a janitor are named Mr. Brown, Mr. Green, Mr. White, and Mr. Black, but not respectively. Four students with the same names will be designated here as Brown, Green, White and Black. The student with the same name as the professor belongs to Black’s fraternity. Mr. Green’s daughter-in-law lives in Philadelphia. The father of one of the students always confuses White and Green in class, but is not absentminded. The janitor’s wife has never seen Mr. Black. Mr. White is the instructor’s father-in-law and has no grandchildren. The president’s oldest son is seven. What are the names of the president, professor, instructor, and janitor?
MR. WHITE - PRESIDENT
MR. BROWN - PROFESSOR
MR. BLACK - INSTRUCTOR
MR. GREEN - JANITOR
LIBERAL ARTS AND ENGINEERING
On a certain campus liberal arts students always lie and engineers always tell the truth. A stranger meets 3 students and asks the first if he is studying liberal arts. The first answers the question, but the stranger doesn’t hear him. The second student then says that the first denied being a liberal arts student. Then the third student says that the first is really a liberal arts student. How many are Iiberal arts students? Can we decide which?
- 1 liberal arts student
First student - Liberal
Second student - Engineering
Third student - Engineering
A, B, C MARKED FOREHEADS
Three men are blindfolded in a mirrorless room. Each is told that he may or may not be given a mark on his forehead, and is instructed that when the blindfolds are removed each is to raise his hand if he sees one or more marked foreheads, and to lower his hand when he rationally concludes whether his own forehead is or is not marked. Unknown to the participants, all foreheads are actually marked, The blindfolds are removed, and all hands are instantly raised. One of the men shortly lowers his hand. By what logical process does he know he is marked?
A knows that he also must be marked
UNREQUITED LOVE
Four boys, Alan, Brian, Charles and Donald, and four girls, Eve, Fay, Gwen and Helen are each in love with one of the others, and, sad to say, in no case is their love requited. Alan loves the girl who loves the man who loves Eve. Fay is loved by the man who is loved by the girl loved by Brian. Charles loves the girl who loves Donald. If Brian is not loved by Gwen, and the boy who is loved by Helen does not love Gwen, who loves Alan?
Gwen loves Alan
CANOE AND COIN ON WATER
A canoe is floating in a swimming pool. Which will raise the level of the water in the pool higher, dropping a penny into the pool or into the canoe? Or does it make any difference?
- It makes difference
- Dropping coin in canoe, will raise water level higher
COCK ROBIN MURDER WHO IS LYING
Five suspects were rounded up in connection with the famous “Cock Robin Murder.” Their statements were as follows:
A: “C and D are lying.”
B: “A and E are lying.”
C: “B and D are lying.”
D: “C and E are lying.”
E: “A and B are lying.”
Who is lying?
A
- if B is telling the truth, D also tells the truth
- if B is lying, C and E are telling the truth.
- Thus both cases, A is lying
ACQUAINTED OR UNACQUAITED
In any gathering of six people prove that either three are mutually acquainted or three are mutually unacquainted.
Call one of them Smith. Say the first, i-e., A, B and C are acquainted with Smith.
- if pair of them are acquainted, the pair and smith are mutually acuquainted.
- if not, A, B, C are mutually unacquaited.
GROCER WEIGHING
Six grocers in a town each sell a different brand of tea in four ounce packets at 25 cents per packet. One of the grocers gives short weight, each packet of his brand weighing only 3 3/4 ounces. If I can use a balance for only one weighing, what is the minimum amount I must spend to be sure of finding the grocer who gives short weight?’
3.7 dollars
KROFLITE AND BEELINE
Between Kroflite and Beeline are five other towns. The seven towns are an integral number of miles from each other along a straight road. The towns are so spaced that if one knows the number of miles a person has traveled between any two towns he can determine the particular towns uniquely. What is the minimum distance between Kroflite and Beeline to make this possible?
- At least 25 miles
RED, GRAY BLACK FLAGSTONES
A man has red, gray and black flagstones for making a walk. He wants no two consecutive stones to be the same color, no consecutive pair of stones to have the same two colors in the same order, no repetition of three consecutive colors, etc. He starts out laying first a red stone, then a gray, and continues until he finishes laying the seventh stone. He then finds himself stymied and unable to use any stone for the eighth without repetition of some color pattern. What were the colors of the first seven stones?
R G R B R G R
SUBTRACT A SQUARE
In the game “subtract-a-square,” a positive integer is written down and two players alternately subtract squares from it with the restriction that the remainder must never be Iess than zero. The player who leaves zero wins. What square should the first player subtract if the original number is 29?
- first player must subtract 9
He then counters his opponents’ plays
of 1, 4, 9, or 16
with 9, 16, 9, or 4
respectively.
