PRACTICAL QUESTIONS IN MATHEMATICS
Besavilla.notes APRIL 2022
1. PROBLEM 11. PROBLEM
Stations A and B are 120 miles apart on a single-track railroad. How A neat computer programmer wears a clean shirt every day. How
far had the fly flown? many shirts must he own to keep him going?
ANS: 300 Ans: 15
12. PROBLEM
2. PROBLEM Very few people are aware of the growth pattern of Jack’s
beanstalk… How long did it take to achieve its maximum height?
A man walks one mile south, one mile west, then one mile north
Ans: 198 days
ending where he begins. From how many points on the surface of
the earth can such journey be made?
ANS: Infinite 13. PROBLEM
Six boys on a hockey team pick a captain by forming a circle … what
number should he choose?
3. PROBLEM Ans: 10
A brick has 8 bricks. Seven of the bricks weigh the same amount…
How can he find the heaviest brick…
ANS: 3, 3, 2 14. PROBLEM
A jig-saw puzzle contains 100 pieces… What is the minimum
number of moves required to complete the puzzle?
4. PROBLEM Ans: 99
Maynard’s Grandfather Clock is driven by two weights, What is
Maynard’s bedtime?
Ans: 9 pm or 3 am 15. PROBLEM
A novice librarian shelved a twelve volume set of encyclopedias…
where will the annual supplement, Volume 13, go?
5. PROBLEM Ans: Between 10 and 3
Dr. Fubisher LaRouche, the noted mathematician, was shoping at a
hardware store… What was Dr. LaRouche buying?
Ans: 10 cent/number 16. PROBLEM
Four players played a hand of hearts at $1 a point… How many
hearts did poor Dave take in?
6. PROBLEM Ans: 4
The numbers are divided into three groups as follows; 0, 3, 6, 8,
9,…. In which groups would 15, 16 and 17 be placed? 17. PROBLEM
Ans: 15 and 16 in the 3rd group In a memorable game with the Podunk Polecats, the Mudville Mets
17 in the 2nd group established a record... How many walks did Podunk allow in that
tedious half-inning?
Ans: 30
7. PROBLEM
In a fast Major League baseball game, pitcher Hi N. Outside
managed to get by with the minimum number of pitches possible… 18. PROBLEM
How many pitches did he make? A Solid State Physicist gives a small stag party. Find the number of
Ans: 25 pitches guests.
Ans: two including the host
8. PROBLEM
19. PROBLEM
State University won their first football game of the season 17 to 0.
A college president, a professor, an instructor, and a janitor are
What were State’s quarter scores?
named… What are the names of the president, professor, instructor,
Ans: 0, 3, 6, 8
and janitor?
Ans: President – white
9. PROBLEM Professor – brown
A chemist has three large test tubes and a beaker with 54 c.c. How Instructor – black
can he retain 50 c.c. in the beaker? Janitor – green
Ans: 50
20. PROBLEM
On a cetain campus liberal arts students always lie and engineers
10. PROBLEM always tell the truth. How many are liberal arts students?
How many colors are necessary for the squares of a chessboard… Ans: ONE
Ans: 8 colors
, 21. PROBLEM 32. PROBLEM
A canoe is floating in a swimming pool. Which will raise the level of On a certain day, our parking lot contains 999 cars, no two of which
the water in the pool higher… have the same 3 digit license number… what is the probability that
Ans: Dropping into the canoe the license numbers of the first 4 cars to leave the parking lot are in
increasing order of magnitude?
22. PROBLEM Ans: 4! = 24 possible permutations of 4 cars
Five suspects were rounded up in connection with the famous”Cock
Robin Murder.” 33. PROBLEM
Ans: A A hospital nursery contains only two baby boys; the girls have not
yet been counted... What is the probability that the last addition to
23. PROBLEM the nursery was a girl?
Six grocers in a town each sell a different brand of tea in four ounce Ans: 2/5
packets at 25 cents per packet... what is the minimum amount I must
spend to be sure of finding the grocer who gives short weight?
Ans: 3.7 dollars 34. PROBLEM
Assume that a single depth cahrge has a probability of ½ of sinking a
submarine… What is the probabilit that 4 depth charges will sink the
24. PROBLEM sub?
Between Kroflite and Beeline are five other towns… What is the Ans: 251/256
minimum distance between Kroflite and Beeline to make this
possible?
Ans: 25 miles 35. PROBLEM
If two marbles are removed at random from a bag containing lack
25. PROBLEM and white marbles… How many marbles are there of each color?
Ans: 6 white, 4 black
In the game “subtract-a-square,” a positive integer… What square
should the first player subtract if the original number is 29?
Ans: 9 36. PROBLEM
Rigorously speaking, two men are “brothers-in-law”… How many
26. PROBLEM men can there be with each man a brother-in-law of every other
A lamp has three on-off buttons, all of which must be on for the lamp man?
to light... In what order did he press the buttons? Ans: 3 men
Ans: 1, 2, 3, 2, 1, 2, 3
37. PROBLEM
27. PROBLEM A salesman visits ten cities arranged in the form of a circle, spending
A game proceeds as follows: Smith starts with a 10-link chain and a day in each… How many days he could be in any one of the ten
removes any single link… What should Smith do first? cities?
Ans: Smith should leave two chains of 6 and 3 links Ans: 83
28. PROBLEM
38. PROBLEM
A list contains 1968 statements, numbered in serial order…
Four swimming pool builders submit sealed bids to a homeowner…
Determine the truth or falsity of each statement.
what procedure will maximize his chances of accepting the lowest
Ans: Statement 1967 is true and all the rest are false
bid, and what will be the probability of doing so?
Ans: Probability of accepting the lowest bid is 11/24, his
29. PROBLEM chance is reduced to 10/24
Hard Knox College is a member of a six-school basketball league…
How did Hard Knox make out?
Ans: He tied for 2nd place with 0.60 39. PROBLEM
Three dart players threw simultaneously at a tic-tac-toe board...
30. PROBLEM What is the probabilit that the three hits constituted a win at tic-tac-
A gambler devised a game to be played with a friend… Did he gain, toe?
lose, or break even? Ans: 2/21
Ans: He lost
40. PROBLEM
31. PROBLEM All the members of a fraternity play basketball while all but one play
A prisoner is given 10 white balls, 10 black balls and two boxes… ice hockey… how many are in the fraternity?
How should the prisoner arrange the balls in the boxes to give Ans: 15
himself the best chance for survival?
Ans: 1 white ball in one box, remaining balls (9 white and 10
black) in the other box. Chance of survival is 73.7%
Besavilla.notes APRIL 2022
1. PROBLEM 11. PROBLEM
Stations A and B are 120 miles apart on a single-track railroad. How A neat computer programmer wears a clean shirt every day. How
far had the fly flown? many shirts must he own to keep him going?
ANS: 300 Ans: 15
12. PROBLEM
2. PROBLEM Very few people are aware of the growth pattern of Jack’s
beanstalk… How long did it take to achieve its maximum height?
A man walks one mile south, one mile west, then one mile north
Ans: 198 days
ending where he begins. From how many points on the surface of
the earth can such journey be made?
ANS: Infinite 13. PROBLEM
Six boys on a hockey team pick a captain by forming a circle … what
number should he choose?
3. PROBLEM Ans: 10
A brick has 8 bricks. Seven of the bricks weigh the same amount…
How can he find the heaviest brick…
ANS: 3, 3, 2 14. PROBLEM
A jig-saw puzzle contains 100 pieces… What is the minimum
number of moves required to complete the puzzle?
4. PROBLEM Ans: 99
Maynard’s Grandfather Clock is driven by two weights, What is
Maynard’s bedtime?
Ans: 9 pm or 3 am 15. PROBLEM
A novice librarian shelved a twelve volume set of encyclopedias…
where will the annual supplement, Volume 13, go?
5. PROBLEM Ans: Between 10 and 3
Dr. Fubisher LaRouche, the noted mathematician, was shoping at a
hardware store… What was Dr. LaRouche buying?
Ans: 10 cent/number 16. PROBLEM
Four players played a hand of hearts at $1 a point… How many
hearts did poor Dave take in?
6. PROBLEM Ans: 4
The numbers are divided into three groups as follows; 0, 3, 6, 8,
9,…. In which groups would 15, 16 and 17 be placed? 17. PROBLEM
Ans: 15 and 16 in the 3rd group In a memorable game with the Podunk Polecats, the Mudville Mets
17 in the 2nd group established a record... How many walks did Podunk allow in that
tedious half-inning?
Ans: 30
7. PROBLEM
In a fast Major League baseball game, pitcher Hi N. Outside
managed to get by with the minimum number of pitches possible… 18. PROBLEM
How many pitches did he make? A Solid State Physicist gives a small stag party. Find the number of
Ans: 25 pitches guests.
Ans: two including the host
8. PROBLEM
19. PROBLEM
State University won their first football game of the season 17 to 0.
A college president, a professor, an instructor, and a janitor are
What were State’s quarter scores?
named… What are the names of the president, professor, instructor,
Ans: 0, 3, 6, 8
and janitor?
Ans: President – white
9. PROBLEM Professor – brown
A chemist has three large test tubes and a beaker with 54 c.c. How Instructor – black
can he retain 50 c.c. in the beaker? Janitor – green
Ans: 50
20. PROBLEM
On a cetain campus liberal arts students always lie and engineers
10. PROBLEM always tell the truth. How many are liberal arts students?
How many colors are necessary for the squares of a chessboard… Ans: ONE
Ans: 8 colors
, 21. PROBLEM 32. PROBLEM
A canoe is floating in a swimming pool. Which will raise the level of On a certain day, our parking lot contains 999 cars, no two of which
the water in the pool higher… have the same 3 digit license number… what is the probability that
Ans: Dropping into the canoe the license numbers of the first 4 cars to leave the parking lot are in
increasing order of magnitude?
22. PROBLEM Ans: 4! = 24 possible permutations of 4 cars
Five suspects were rounded up in connection with the famous”Cock
Robin Murder.” 33. PROBLEM
Ans: A A hospital nursery contains only two baby boys; the girls have not
yet been counted... What is the probability that the last addition to
23. PROBLEM the nursery was a girl?
Six grocers in a town each sell a different brand of tea in four ounce Ans: 2/5
packets at 25 cents per packet... what is the minimum amount I must
spend to be sure of finding the grocer who gives short weight?
Ans: 3.7 dollars 34. PROBLEM
Assume that a single depth cahrge has a probability of ½ of sinking a
submarine… What is the probabilit that 4 depth charges will sink the
24. PROBLEM sub?
Between Kroflite and Beeline are five other towns… What is the Ans: 251/256
minimum distance between Kroflite and Beeline to make this
possible?
Ans: 25 miles 35. PROBLEM
If two marbles are removed at random from a bag containing lack
25. PROBLEM and white marbles… How many marbles are there of each color?
Ans: 6 white, 4 black
In the game “subtract-a-square,” a positive integer… What square
should the first player subtract if the original number is 29?
Ans: 9 36. PROBLEM
Rigorously speaking, two men are “brothers-in-law”… How many
26. PROBLEM men can there be with each man a brother-in-law of every other
A lamp has three on-off buttons, all of which must be on for the lamp man?
to light... In what order did he press the buttons? Ans: 3 men
Ans: 1, 2, 3, 2, 1, 2, 3
37. PROBLEM
27. PROBLEM A salesman visits ten cities arranged in the form of a circle, spending
A game proceeds as follows: Smith starts with a 10-link chain and a day in each… How many days he could be in any one of the ten
removes any single link… What should Smith do first? cities?
Ans: Smith should leave two chains of 6 and 3 links Ans: 83
28. PROBLEM
38. PROBLEM
A list contains 1968 statements, numbered in serial order…
Four swimming pool builders submit sealed bids to a homeowner…
Determine the truth or falsity of each statement.
what procedure will maximize his chances of accepting the lowest
Ans: Statement 1967 is true and all the rest are false
bid, and what will be the probability of doing so?
Ans: Probability of accepting the lowest bid is 11/24, his
29. PROBLEM chance is reduced to 10/24
Hard Knox College is a member of a six-school basketball league…
How did Hard Knox make out?
Ans: He tied for 2nd place with 0.60 39. PROBLEM
Three dart players threw simultaneously at a tic-tac-toe board...
30. PROBLEM What is the probabilit that the three hits constituted a win at tic-tac-
A gambler devised a game to be played with a friend… Did he gain, toe?
lose, or break even? Ans: 2/21
Ans: He lost
40. PROBLEM
31. PROBLEM All the members of a fraternity play basketball while all but one play
A prisoner is given 10 white balls, 10 black balls and two boxes… ice hockey… how many are in the fraternity?
How should the prisoner arrange the balls in the boxes to give Ans: 15
himself the best chance for survival?
Ans: 1 white ball in one box, remaining balls (9 white and 10
black) in the other box. Chance of survival is 73.7%
