ENGR. BESAVILLA’S NOTES
Problem 73 Problem 81
A sharp operator makes the following deal. A player is to toss a coin and Two men are walking towards each other at the side of a railway. A freight
receive 1, 4, 9, ….. n2 dollars if the first head comes up on the first, second, train overtakes one of them in 20 seconds and exactly ten minutes later
third,… n-th toss. The sucker pays ten dollars for this. How much can the meets the other man coming in the opposite direction. The train passes this
operator expect to make if this repeated a great many times? man in 18 seconds. How long after the train has passed the second man will
the two men meet? (Constant speeds are to be assumed throughout.)
Ans: $4 per game
Ans: 5562
Problem 74
In 1969, the World Series began in the stadium of the American League Problem 82
pennant winner. Assume the contenders are evenly matched. What is the Using the French Tricolor as a model, how many flags are possible with five
probability that the series ended where it began? available colors if two adjacent rows must not be colored the same?
Ans: 5/8 Ans: 50 flags
Problem 75 Problem 83
In a carnival game 5 balls are tossed into a square box divided into 4 square A cubic box with sides ‘a’ feet long is placed flag against a wall. A ladder ‘p’
cells, with baffles to insure that every ball has an equal chance of going in feet long is placed in such a way that it touches the wall as well as the free
any cell. The player pays $1 and receives $1 for every cell which is empty horizontal edge of the box. If a = 1 and p = 15, calculate at what height
after the 5 balls are thrown. How much does the operator expect to make per
game? the ladder touches the wall, using quadratics only.
Ans: 1.38 ft. or 3.62 ft.
Ans: a nickel/game
Problem 84
Problem 76
Citizens of Franistan pay as much income tax (percentage-wise) as they
Having lost a cheker game, a specialist in learning programs threw one of he
make rupees per week. What is the optimal salary in Franistan?
red checkers out the window. His wife reboxed the 12 black pieces and 11
red pieces one at a time in random fashion. The number of black checkers in Ans: 50 rupees
the box always exceeded the number of reds. What was the a priori
probability of this occurrence? Problem 85
Ans: 1/23 Two snails start from the same point in opposite directions toward two bits of
food. Each reaches his destination in one hour. If each snail had gone in
direction the other took, the first snail would have reached his food 35
Problem 77 minutes after the second. How do their speeds compare?
An expert on transformer design relaxed one Saturday by going to the races.
At the end of the first race he had doubled his money. He bet $30 on the 3
second race and tripled his money. He bet $54 on the third race and
Ans: V1 = V2
4
quadrupled his money. He bet $72 on the fourth race and lost it, but still had
$48 left. With how much money did he start?
Problem 86
Ans: 29 A necklace consists of pearls which increase uniformly from a weight of 1
carat for the end pearls to a weight of 100 carats for the middle pearl. If the
Problem 78 necklace weighs altogether 1650 carats and the clasp and string together
There are n points on a circle. A straight line segment is drawn between weigh as much (in carats) as the total number of pearls, how many pearls
each pair of points. How many intersections are there within the circle if no 3 does the necklace contain?
lines are collinear? Ans: 33 pearls
Ans: 764,488
Problem 87
A pupil wrote on the blackboard a series of fractions having positive integral
Problem 79
terms and connected by signs which were either all + or all x, although they
Dr. Reed, arriving late at the lab one morning, pulled out his watch and the
were so carelessly written it was impossible to tell which they were. It still
hour hand are exactly together every sixty-five minutes.” Does Dr. Reed’s
wasn’t clear even though he announced the result of the operation at every
watch gain or lose, and how much per hour?
step. The third fraction had denominator 19. What was the numerator?
Ans: Gains 60/143 minutes Ans: Numerator = 25
Problem 80 Problem 88
At this moment, the hands of a clock in the course of normal operation
Jai Alai balls come in boxes of 8 and 15; so that 38 balls (one small box and
describe a time somewhere between 4:00 and 5:00 on a standard clock face.
two large) can be bought without having to break open a box, but not 39.
Within one hour or less, the hands will have exactly exchanged positions;
What is the maximum number of balls which cannot be bought without
what time is it now?
breaking boxes?
Ans: 4:26.853
Ans: 97 balls
Problem 73 Problem 81
A sharp operator makes the following deal. A player is to toss a coin and Two men are walking towards each other at the side of a railway. A freight
receive 1, 4, 9, ….. n2 dollars if the first head comes up on the first, second, train overtakes one of them in 20 seconds and exactly ten minutes later
third,… n-th toss. The sucker pays ten dollars for this. How much can the meets the other man coming in the opposite direction. The train passes this
operator expect to make if this repeated a great many times? man in 18 seconds. How long after the train has passed the second man will
the two men meet? (Constant speeds are to be assumed throughout.)
Ans: $4 per game
Ans: 5562
Problem 74
In 1969, the World Series began in the stadium of the American League Problem 82
pennant winner. Assume the contenders are evenly matched. What is the Using the French Tricolor as a model, how many flags are possible with five
probability that the series ended where it began? available colors if two adjacent rows must not be colored the same?
Ans: 5/8 Ans: 50 flags
Problem 75 Problem 83
In a carnival game 5 balls are tossed into a square box divided into 4 square A cubic box with sides ‘a’ feet long is placed flag against a wall. A ladder ‘p’
cells, with baffles to insure that every ball has an equal chance of going in feet long is placed in such a way that it touches the wall as well as the free
any cell. The player pays $1 and receives $1 for every cell which is empty horizontal edge of the box. If a = 1 and p = 15, calculate at what height
after the 5 balls are thrown. How much does the operator expect to make per
game? the ladder touches the wall, using quadratics only.
Ans: 1.38 ft. or 3.62 ft.
Ans: a nickel/game
Problem 84
Problem 76
Citizens of Franistan pay as much income tax (percentage-wise) as they
Having lost a cheker game, a specialist in learning programs threw one of he
make rupees per week. What is the optimal salary in Franistan?
red checkers out the window. His wife reboxed the 12 black pieces and 11
red pieces one at a time in random fashion. The number of black checkers in Ans: 50 rupees
the box always exceeded the number of reds. What was the a priori
probability of this occurrence? Problem 85
Ans: 1/23 Two snails start from the same point in opposite directions toward two bits of
food. Each reaches his destination in one hour. If each snail had gone in
direction the other took, the first snail would have reached his food 35
Problem 77 minutes after the second. How do their speeds compare?
An expert on transformer design relaxed one Saturday by going to the races.
At the end of the first race he had doubled his money. He bet $30 on the 3
second race and tripled his money. He bet $54 on the third race and
Ans: V1 = V2
4
quadrupled his money. He bet $72 on the fourth race and lost it, but still had
$48 left. With how much money did he start?
Problem 86
Ans: 29 A necklace consists of pearls which increase uniformly from a weight of 1
carat for the end pearls to a weight of 100 carats for the middle pearl. If the
Problem 78 necklace weighs altogether 1650 carats and the clasp and string together
There are n points on a circle. A straight line segment is drawn between weigh as much (in carats) as the total number of pearls, how many pearls
each pair of points. How many intersections are there within the circle if no 3 does the necklace contain?
lines are collinear? Ans: 33 pearls
Ans: 764,488
Problem 87
A pupil wrote on the blackboard a series of fractions having positive integral
Problem 79
terms and connected by signs which were either all + or all x, although they
Dr. Reed, arriving late at the lab one morning, pulled out his watch and the
were so carelessly written it was impossible to tell which they were. It still
hour hand are exactly together every sixty-five minutes.” Does Dr. Reed’s
wasn’t clear even though he announced the result of the operation at every
watch gain or lose, and how much per hour?
step. The third fraction had denominator 19. What was the numerator?
Ans: Gains 60/143 minutes Ans: Numerator = 25
Problem 80 Problem 88
At this moment, the hands of a clock in the course of normal operation
Jai Alai balls come in boxes of 8 and 15; so that 38 balls (one small box and
describe a time somewhere between 4:00 and 5:00 on a standard clock face.
two large) can be bought without having to break open a box, but not 39.
Within one hour or less, the hands will have exactly exchanged positions;
What is the maximum number of balls which cannot be bought without
what time is it now?
breaking boxes?
Ans: 4:26.853
Ans: 97 balls
