ENGR. BESAVILLA’S NOTES
Problem 31 Problem 37
A college president, a professor, an instructor, and a janitor are named Mr. Between Kroflite and Beeline are five other towns. The seven towns are an
Brown, Mr. Green, Mr. White, and Mr. Black, but not respectively. Four integral number of miles from each other along a staight road. The towns are
students with the same names will be designated here as Brown, Green, so spaced that if one knows the number of miles a person has traveled
White and Black. The student with the same name as the professor belongs between any two towns he can determine the particular towns uniquely.
to Black’s fraternity. Mr. Green’s daughter-in-law lives in Philadelphia. The What is the minimum distance between Kroflite and Beeline to make this
father of one of the students always confuses White and Green in class, but possible?
not absentminded. The janitor’s wife has never seen Mr. Black. Mr. White is
Ans: 25 miles
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? Problem 38
Ans: President – white In the game “subtract-a-square,” a positive integer is written down and two
Professor – brown players alternately subtract squares from it with the restriction that the
Instructor – black remainder must never be less than zero. The player who leaves zero wins.
What square should the first player subtract if the original number is 29?
Janitor – green
Ans: 9
Problem 32
On a cetain campus liberal arts students always lie and engineers always tell Problem 39
the truth. A stranger meets 3 students and asks the first if he is studying A lamp has three on-off buttons, all of which must be on for the lamp to light.
liberal arts. The first answers the question, but the stranger doesn’t hear him. A man wishes to turn on the lamp at a moment when only the second switch
The second student then says that the first denied being a liberal arts is off. He does not know this and proceeds to press the first button. Getting
student. Then the third student says that the first is really a liberal arts no result he presses the second and eventually, on the seventh trial, (never
student. How many are liberal arts students? Can we decide which? repeating any on-off configuration), the lamp finally lights. In what order did
he press the buttons?
Ans: ONE
Ans: 1, 2, 3, 2, 1, 2, 3
Problem 33
Problem 40
Four boys, Alan, Brian, Charles and Donald, and four girls, Eve, Fay, Gwen
A game proceeds as follows: Smith starts with a 10-link chain and removes
and Helen are each in love with one of the others, and, sad to say, in no
any single link, presenting Jones either with a 9-link chain or two chains
case is their love requited. Alan loves the girl who loves the man who loves
having a total of 9 links. Jones removes any one link from each of the chains.
Eve. Fay is loved by the man who loves Donald. If Brian is not loved by
Smith removes any one link from each of the remaining chains and so on,
Gwen, and the boy who is loved by Helen does not love Gwen, who loves
until the winner removes the last link or links. What should Smith do first?
Alan?
Ans: Gwen loves Alan Ans: Smith should leave two chains of 6 and 3 links
Problem 34 Problem 41
In the country of Puevigi, the population consists of Soothsayers, who never
A canoe is floating in a swimming pool. Which will raise the level of the water
lie, Dissemblers, who always lie, and Diplomats, who alternately lie and tell
in the pool higher, dropping a penny into the pool or into the canoe? Or does
the truth. If you meet a citizen of Puevigi, how with just two questions can
it make any difference?
you determine to which group he belongs?
Ans: Dropping into the canoe will raise the water level higher.
Ans: First question should be:
Will your answer to my second question be true?
Problem 35
If he answers No, he is a diplomat.
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 Second question:
E are lying.” C: “B and D are lying.” D: “C and E are lying.” E: “A and B are Are you a diplomat?
lying.” Who is lying? If he answers yes, he is a Dissembler.
If he says No, he si a Soothsayers.
Ans: A
Problem 42
Problem 36
A teenager wants to go out 2 consecutive nights out of a 3-day weekend.
Six grocers in a town each sell a different brand of tea in four ounce packets
Permission for each night is obtained (or denied) by asking either Father or
at 25 cents per packet. One of the grocers gives short weight, each packet of
Mother. Father is known to be more likely to grant permission. However, if
his brand weighing only 3 ¾ ounces. If I can use a balance for only one
the same parent is asked on 2 consecutive days the answers are never the
weighing, what is the minimum amount I must spend to be sure of finding the
same 2 days running. Whom should he ask first?
grocer who gives short weight?
Ans: Mother
Ans: 3.7 dollars
Problem 31 Problem 37
A college president, a professor, an instructor, and a janitor are named Mr. Between Kroflite and Beeline are five other towns. The seven towns are an
Brown, Mr. Green, Mr. White, and Mr. Black, but not respectively. Four integral number of miles from each other along a staight road. The towns are
students with the same names will be designated here as Brown, Green, so spaced that if one knows the number of miles a person has traveled
White and Black. The student with the same name as the professor belongs between any two towns he can determine the particular towns uniquely.
to Black’s fraternity. Mr. Green’s daughter-in-law lives in Philadelphia. The What is the minimum distance between Kroflite and Beeline to make this
father of one of the students always confuses White and Green in class, but possible?
not absentminded. The janitor’s wife has never seen Mr. Black. Mr. White is
Ans: 25 miles
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? Problem 38
Ans: President – white In the game “subtract-a-square,” a positive integer is written down and two
Professor – brown players alternately subtract squares from it with the restriction that the
Instructor – black remainder must never be less than zero. The player who leaves zero wins.
What square should the first player subtract if the original number is 29?
Janitor – green
Ans: 9
Problem 32
On a cetain campus liberal arts students always lie and engineers always tell Problem 39
the truth. A stranger meets 3 students and asks the first if he is studying A lamp has three on-off buttons, all of which must be on for the lamp to light.
liberal arts. The first answers the question, but the stranger doesn’t hear him. A man wishes to turn on the lamp at a moment when only the second switch
The second student then says that the first denied being a liberal arts is off. He does not know this and proceeds to press the first button. Getting
student. Then the third student says that the first is really a liberal arts no result he presses the second and eventually, on the seventh trial, (never
student. How many are liberal arts students? Can we decide which? repeating any on-off configuration), the lamp finally lights. In what order did
he press the buttons?
Ans: ONE
Ans: 1, 2, 3, 2, 1, 2, 3
Problem 33
Problem 40
Four boys, Alan, Brian, Charles and Donald, and four girls, Eve, Fay, Gwen
A game proceeds as follows: Smith starts with a 10-link chain and removes
and Helen are each in love with one of the others, and, sad to say, in no
any single link, presenting Jones either with a 9-link chain or two chains
case is their love requited. Alan loves the girl who loves the man who loves
having a total of 9 links. Jones removes any one link from each of the chains.
Eve. Fay is loved by the man who loves Donald. If Brian is not loved by
Smith removes any one link from each of the remaining chains and so on,
Gwen, and the boy who is loved by Helen does not love Gwen, who loves
until the winner removes the last link or links. What should Smith do first?
Alan?
Ans: Gwen loves Alan Ans: Smith should leave two chains of 6 and 3 links
Problem 34 Problem 41
In the country of Puevigi, the population consists of Soothsayers, who never
A canoe is floating in a swimming pool. Which will raise the level of the water
lie, Dissemblers, who always lie, and Diplomats, who alternately lie and tell
in the pool higher, dropping a penny into the pool or into the canoe? Or does
the truth. If you meet a citizen of Puevigi, how with just two questions can
it make any difference?
you determine to which group he belongs?
Ans: Dropping into the canoe will raise the water level higher.
Ans: First question should be:
Will your answer to my second question be true?
Problem 35
If he answers No, he is a diplomat.
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 Second question:
E are lying.” C: “B and D are lying.” D: “C and E are lying.” E: “A and B are Are you a diplomat?
lying.” Who is lying? If he answers yes, he is a Dissembler.
If he says No, he si a Soothsayers.
Ans: A
Problem 42
Problem 36
A teenager wants to go out 2 consecutive nights out of a 3-day weekend.
Six grocers in a town each sell a different brand of tea in four ounce packets
Permission for each night is obtained (or denied) by asking either Father or
at 25 cents per packet. One of the grocers gives short weight, each packet of
Mother. Father is known to be more likely to grant permission. However, if
his brand weighing only 3 ¾ ounces. If I can use a balance for only one
the same parent is asked on 2 consecutive days the answers are never the
weighing, what is the minimum amount I must spend to be sure of finding the
same 2 days running. Whom should he ask first?
grocer who gives short weight?
Ans: Mother
Ans: 3.7 dollars
