LITTONS 2
A pirate buried his treasure on an island, a conspicuous landmark of which were three palm trees, each one 100 feet from the other two. Two of these trees were in a N-S Jine. The directions for finding the treasure read: "Proceed from southernmost tree 15 feet due north, then 26 feet due west." Is the treasure. buried within the triangle formed by the trees?
The treasure will lie outside the triangle
The Ben Azouli are camped at an oasis 45 miles west of Taqaba. They decide to dynamite the Trans-Hadramaut railroad joining Taqaba to Maqaba, 60 miles north of the oasis. If the Azouli can cover 18 miles a day, how long will it take them to reach the railroad?
13 ft 5 in
A cross section through the center of a football is a circle x inches in circumference. The football is x-8 inches long from tip to tip and each seam is an arc of a circle 4 x inches in diameter. Find x.
20.69
A coffee pot with a circular bottom tapers uniformly to a circular top with radius half that of the base. A mark halfway up the side says "2 cups." Where should the "3 cups" mark go?
About 2% of the way down from the top of the pot
About 2% of the way down from the top of the pot
About 2% of the way down from the top of the pot
About 2% of the way down from the top of the pot
An icicle forming from a dripping gutter is in the shape of a cone five times as long as it is wide (at the top). A few hours later it has doubled in length and the generating angle has also doubled. How does its present weight compare with its previous weight?
33 times
A student beginning the study of trigonometry came across an expression of the form sin (X + Y). He evaluated this as sin X + sin Y. Surprisingly he was correct. The values of X and Y differed by 10°; what were these values, assuming that 0° <XY < 360°?
175° and 185°
What is the longest 6' wide shuffie board court which will fit in a 20'x 30' rectangular room?
30 7/8 ft
Three farmers, Adams, Brown and Clark all have farms containing the same number of acres. Adams' farm is most nearly square, the length being only 8 miles longer than the width. Clark has the most oblong farm, the length being 34 miles longer than the width. Brown's farm is intermediate between these two, the length being 28 miles longer than the width. If all the dimensions are in exact miles, what is the size of each farm?
40×48, 32×60, and 30×64
1960 and 1961 were bad years for ice cream sales but 1962 was very good. An accountant was looking at the tonnage sold in each and noticed that the digital sum of the tonnage sold in 1962 was three times as much as the digital sum of the tonnage sold in 1961. Moreover, if the amount sold in 1960 (346 tons), was added to the 1961 tonnage, this total was less than the total tonnage sold in 1962 by the digital sum of the tonnage sold in that same year. Just how many more tons of ice cream were sold in 1962 than in the previous year?
361 tons
Three rectangles of integer sides have identical areas. The first rectangle is 278 feet longer than wide. The second rectangle is 96 feet longer than wide. The third rectangle is 542 feet longer than wide. Find the area of the rectangle.
1,466,640
Every year an engineering consultant pays a bonus of $300 to his most industrious assistant, and $75 each to the rest of his staff. After how many years would his outlay be exactly $6,000 if all but two of his staff had merited the $300 bonus, but none of them more than twice?
8 years
Two wheels in the same plane are mounted on shafts 13 in. apart. A belt goes around both wheels to transmit power from one to the other. The radii of the two wheels and the length of the belt not in contact with the wheels at any moment are all integers. How much larger is one wheel than the other?
5 inches
Dad and his son have the same birthday. On the last one, Dad was twice as old as Junior. Uncle observed that this was the ninth occasion on which Dad's birthday age had been an integer multiple of Junior's. How old is Junior?
36
The undergraduates of a School of Engineering wished to form ranks for a parade. In ranks of 3 abreast, 2 men were left over; in ranks of 5, 4 over; in 7's, 6 over; and 11's, 10 over. What is the least number of marchers there must have been?
1154
The sum of the digits on the odometer in my car (which reads up to 99999.9 miles) has never been higher than it is now, but it was the same 900 miles ago. How many miles must I drive before it is higher than it is now?
100 miles
A rectangular picture, each of whose dimensions is an integral number of inches, has an ordinary rectangular frame 1 inch wide. Find the dimensions of the picture if the area of the picture and the area of the frame are equal.
3×10 or 4×6
3×10 or 4×6
My house is on a road where the numbers run 1,2,3,4... consecutively. My number is a three digit one and, by a curious coincidence, the sum of all house numbers less than mine is the same as the sum of all house numbers greater than mine. What is my number and how many houses are there on my road?
#204 and 288 houses
On what days of the week can the first day of a century fall? (The first day of the twentieth century was Jan. 1, 1901)
Monday
No factorial can end in five zeros. What is the next smallest number of zeros in which a factorial can not end?
11
A ball is dropped from a height of 10 feet. It rebounds one-half the distance on each bounce. What is the total distance it travels?
30 ft
Mr. X veers to the right when he walks. The curvature of his path is proportional to his latitude. He starts walking North from point A on the equator, in the area of a large level plain, and finds he is proceeding East when he is one mile north of the equator. He continues walking and arrives back at the equator at point B. What is the straight line distance from A to B?
1.2 miles
A boat owner agrees to take a group on an outing at $4.50 a piece if the number of passengers is equal to or less than his break- even point. For each person above this he reduces the fare for all passengers 3 cents per person. If he has on board now the number of passengers that maximizes the total collected, what is the boat owner's profit?
0
The price per cubic inch for platinum trays is the same as that per square inch for platinum sheets. A metal supply house has a square of platinum which will yield the same amount whether sold as a sheet, or fashioned into a tray of maximum volume with the four cut-out corners sold as sheets. How big is the square?
1 ft