LITTONS 1
Rufus T. Flypaper drives two miles to work every morning. Very precise, he knows he must average 30 mph to arrive on time. One morning a woman driver impedes him for the first mile, cutting his average to only 15 mph. He quickly calculated his proper speed for the rest of the trip to arrive on time. Assume that his car could do 120 mph. Could he arrive on time?
No, he has already used 4 minutes
Station A and B are 120 miles apart on a single-track railroad. At the same time a train leaves A for B at 15 mph. Just as the first train leaves A, a South American botfly flies from the front of the engine straight toward the other train at 100 mph. On meeting the second train it immediately turns back and flies straight for the first train. It continues to fly back and fourth with undiminished speed until jt is crushed in the eventual collision. How far had the fly flown?
300 miles
Assuming the sun rises at 6:00 am, sets at 6:00 pm, and moves at a uniform rate, how can a lost boy scout determine south by means of a watch on a cloudless days?
Align the hour hand with the sun's azimuth, and south will be midway between the hour hand and 12
What is the least number of links that must be disengaged from a 23-link chain so that any number of links from 1 to 23 can be obtained by taking one or more of the pieces?
2
A neat computer programmer wears a clean shirt every day. If he drops off his laundry and picks up the previous week's load every Monday night, how many shirts must he own to keep going?
15
The passenger on an excursion bus consisted of 14 married couple, 8 of whom brought no children, and 6 of whom brought 3 children a piece. Counting the driver, the bus had 31 occupants. How is this possible?
Included among the 18 children were 8 married couples
Very few people are aware of the growth pattern of Jack's beanstalk. On the first day, it increased its height by 1/2, on the second day by 1/3, on the third day by 1/4, and so on. How long did it take to achieve its maximum height (100 times its original height)?
198 days
What operation can be performed the successive times on a solid cube, so that at each stage, the surface area is reduced in the same proportion as the volume?
Turning
A lighthouse shows successive one-second flashes of red, white, green, green, white, red. A second lighthouse does the same with only two-second flashes. The six-second sequence of the first lighthouse is repeated steadily, as it the twelve-second sequence of the other lighthouse. What fraction of the time do the two lights show the same color if the given sequences start at the same time?
1/6
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
Six Grocers in a town each sell a different brand of tea in four ounce packets at 25 cents per packet. Once the grocers gives short weight, each packet of his brand weighing on 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
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?
25 miles
In Bristol, 90% of the citizen drink tea; 80% drink coffee; 70% drink whiskey; and 60% drink gin. No one drinks all four beverages. What percent of Bristol's citizens drinks liquor?
100%
You and a friend spot a loose $20 bill simultaneously and agree to an auction in which you write down your bids and compare them. High bidder gets the $20 and pays the other the amount of the higher bid. Tie bidders split the $20. How much do you bid?
$9.99
A prisoner is given 10 white balls, 10 black balls and two boxes. He is told that an executioner will draw one ball from one of the two boxes. If it is white, the prisoner will go free; if it is black, he will die. How should the prisoner arrange the balls in the boxes to give himself the best chance for survival?
73.7%
Smith and Jones, both 50% marksmen, decided to fight a duel in which they exchange alternate shot until one is hit. What are the odds in favor of the man who shoots first?
2/3
On a certain day, our parking lot contains 999 cars, no two of which have the same 3 digit license number. After 5:00 pm, what is the probability that the license numbers of the first 4 cars to leave the parking lot are in increasing order of magnitude?
24
Three marksmen simultaneously shoot at and hit a rapidly spinning spherical target. What is the probability that the three points of impact are on the same hemisphere?
1
A hospital nursery contains only two baby boys; the girls have not yet been counted. At 2:00 pm, a new baby is added to the nursery. A baby is then selected at random to be the first to have its footprint taken. It turns out to be a boy. What is the probability that the last addition to the nursery was a girl?
2/5
Assume that a depth charge has a probability of 1/2 of sinking a submarine, 1/4 of damage and 1/4 of missing. Assume also that two damaging explosions sink the sub. What is the probability that a 4 depth charge will sink the sub?
251/256
If 2 marbles are removed at random from a bag containing black and white marbles, the chance that they are both white is 1/3. If 3 are removed at random, the chance that they are all white is 1/6. How many marbles are there of each color?
6 whites, 4 blacks
A coin is so unbalance that you are likely to get two heads in two successive throws as you are to get tails in one. What is the probability of getting heads in a single throw?
0.618
All the members of a fraternity play basketball while all but one plays ice hockey; yet the number of possible basketball teams (5 members) is the same as the number of possible ice hockey teams (6 members). Assuming there are enough members for either type of team, how many are in the fraternity?
15
There are three families, each with two sons and two daughters. In how many ways can all these young people be married?
80
How many three digit telephone area codes are possible given that:
(a) the first digit must not be zero or one;
(b) the second digit must be zero of one;
(c) the third digit must not be zero;
(d) the third digit may be one only if the second digit is zero.
136
The local weather forecaster says "no rain" and his record is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain and their record is 3/4. With no other data available, what is the chance of rain?
3/5
To stimulate his son in the pursuit of partial differential equations, math professor offered to pay him $8 for every equation correctly solved and to fine him $5 for every incorrect solution. At the end of 26 problems, neither owned any money to the other. How many did the boy solve correctly?
10
An expert on transformer design relaxed one Saturday by going to the races. At the end of the race, he had doubled his money. He bet $30 on the second race and tripled his money. He bet $54 on the third race and 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?
29
Two men are walking towards each other at the side of a railway. A freight train overtakes one of them in 20 seconds and exactly ten minutes later meets the other man coming in the opposite direction. The train passes this 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)
5562
A cubic box with sides 'a' feet long is placed flat against a wall. A ladder 'p' feet long is placed in such a way that it touches the wall as well as the free horizontal edge of the box. If a = 1 and p = √15, calculate at what height the ladder touches the wall, using quadratics only.
3.62 or 1.38
Dr. Irving Weiman, who is always in a hurry, walks up an up-going escalator at the rate of one step per second. Twenty steps bring him to the top. Next day he goes up to two steps per second, reaching the top in 32 steps. How many steps are there in the escalator?
80
There are nine cities which served by two competing airlines. One or the other airline (but not both) has a flight between every pair of cities. What is the minimum number of triangular flights (i.e., trips from A to B to C and back to A on the same airline)?
12
Two snail 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 the direction the other took, the first snail would have reached his food 35 minutes after the second. How do their speeds compare?
The first snail traveled at three-fourths the speed of the second
A necklace consists of pearls which increase uniformly from a weight of 1 carat for the end pearl to a weight of 100 carats for the middle pearl. If the necklace weighs altogether 1650 carats and the clasp and string together as much (in carat) as the total number of pearls, how many pearls does the necklace contain?
33
Mr. field, a speeder, travelers on a busy highway having the same rate of traffic flow in EW each direction. Except for Mr. Field, the traffic is moving at the legal speed limit. Mr. Field KLING passes one car for every nine which he meets from the opposite direction. By what percentage is he exceeding the speed limit?
25%
The teacher marked the quiz on the following basis: one point for each correct answer, one point off for each question left black and two points off for each question answered incorrectly. Pat made four times as many errors as Mike, But Mike left nine more questions Black. If they both got the same score, how many errors did each make?
Pat: 8, Mike: 2
A student, just beginning the study of logarithms, was required to evaluate log A expression of the form. He proceeded to log B cancel common factors in both numerator and denominator. (including the "factor" log), and arrived at the result 2/3. Surprisingly, this was correct. What were the values of A and B?
A= 9/4 and B= 27/8
There are four towns at the corners of a square. Four motorists set out, each driving to the next (clockwise) town, and each man but the fourth going 8mi./hr. faster than the car ahead thus the first car travels 24mi./hr. faster than the fourth. At the end of one hour the first and third cars are 204, and the second and fourth 212 (beeline) miles apart. How fast is the first car traveling and how far apart are the towns?
50 mi/hr and 180 miles
A pencil, eraser and notebook together cost $1.00. A notebook cost more than two pencil, and three pencils cost more than four erasers. f three erasers cost more than a notebook, how much does each cost?
P= 26, E= 19, and N= 55
The faces of a solid figure are all triangles. The figure has nine vertices. At each of six of these vertices, four faces meet, and at each of the other three vertices, six faces meet. How many faces does the figure have?
14
A new kind of atom smasher is to be composed of two tangents and a circular arc which is concave towards the point of intersection of the two tangents. Each tangent and the arc of the circle is I mile long. What is the radius of the circle?
1437.45 ft
A spider and a fly are located at opposite vertices of a room of dimensions 1,2 and 3 units. Assuming that the fly is too terrified to move, find the minimum distance the spider must crawl to reach the fly.
√18
In a room 40 feet long, 20 feet 20% wide, and 20 feet high, a bug sits on an end wall at a point one foot from the floor, midway between the sidewalls. He decides to go on a journey to a point on the other end wall which is one foot from the ceiling midway between the EW sidewalls. Having no wings, the bug must make this trip by sticking to the surfaces of the room. What is the shortest route that the bug can take?
58 ft
A farmer owned a square field measuring exactly 2261 yards on each side. 1898 yards from one corner and 1009 yards from an adjacent corner stood a beech tree. A neighbor offered to purchase a triangular portion of the field stipulating that a fence should be erected in a straight line from one side of the field to an adjacent side so that the beech tree was part of the fence. The farmer accepted the offer but made sure that the triangular portion was of minimum area. What was the area of the field the neighbor received, and how long was the fenced?
A= 919,120 and L= 2018
A man leaves from the point where the prime meridian crosses the equator and moves forty- five degrees northeast by geographic compass which always points toward the north geographic pole. He constantly corrects his route. Assuming that he walks with equal facility on land and sea, where does he end up and how far will he have travelled when he gets there?
√2×10^7 meters
Near the town of Lunch, Nebraska there is a large triangular plot of land bounded by three straight roads which are 855, 870, and 975 yards long respectively. The owner of the land, a friend of mine, told me that he had decided to sell half the plot to a neighbor, but that the buyer had stipulated that the seller of the land should erect the fence which was to be a straight one. The cost of fences being high, my friend naturally wanted the fence to be as short as possible. What is the minimum length the fence can be?
600 yards
Three hares are standing in a triangular field which is exactly 100 yards on each side. One hare stands at each corner; and simultaneously all three set off running. Each hare runs after the hare in the adjacent corner on his left, thus following a curved course which terminates in the middle of the field, all three hares arriving there together. The hares obviously ran at the same speed, but just how far did they run?
100 yards
A one-acre field in the shape of a right triangle has a post at the midpoint of each side. A sheep is tethered to each of the side posts and a goat to the post on the hypotenuse. The ropes are just long enough to let each animal reach the two adjacent vertices. What is the total area the two sheep have to themselves, i.e", the area the goat cannot reach?
1 acre
A divided highway goes under a number of bridges, the arch over each lane being in the form of a semi-ellipse with the height equal to the width. A truck is 6 ft. wide and 12 ft. high. What is the lowest bridge under which it can pass?
13 ft 5 in
A cowboy is five miles south ot a stream which flows due east. He is also 8 miles west and 6 miles north of his cabin. He wishes to water his horse at the stream and return home. What is the shortest distance he can travel and accomplish this?
17.9 miles