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40 Pound Rock Problem
A farmer has a 40 pound rock which he uses to measure 40 pounds of grain at a time on a giant balance
scale. One day, he drops the rock and it breaks into four pieces. “Never mind,” he said, “now I can measure
any amount of grain from one to forty pounds.” What are the weights of the four pieces?
Checkerboard
How many total squares are on a 8 by 8 checkerboard?
Applicant
Three intelligent women were applying for a computer job for which they were equally qualified, the
interviewer, who was also pretty smart and liked games of logic (She was a retired math teacher), decided that the job would
go to the applicant who could first solve this problem:
The interviewer said: “I will blindfold you and place a mark on each of your foreheads.
Each of you will either have a black or a gray mark. When I tell you to take your blindfolds off, you are to raise your hand
if you see a black mark on the foreheads of either of the applicants. The first one that correctly tells the color of your
own mark will get the job.”
All three women raised their hands at the same time. One of them, however, came up with the
correct color of her own mark. What color is her mark, and how did she figure it out?
The Coconut Problem
There is a desert island on which the only trees are coconut palms. Although it is occasionally visited
by birds, its sole mammal inhabitant is a single monkey, which has been stranded there for many years. The monkey lives on
coconuts. Since dangerous reefs are nearby, sailors are shipwrecked on the island. Fortunately, they can live on the coconuts
until they are rescued. One year, three sailors are ship wrecked on the island; a captain, a midshipman and a common swab.
The captain decides that the coconuts then available on the ground should be divided by rank. He takes half of the available
coconuts, plus half a coconut. He allots half of the remaining coconuts to the midshipman, plus half a coconut. The swab also
gets half the coconuts that are left plus half a coconut. There is still one coconut remaining, so it is tossed to the grateful
monkey, since it is clear that more coconuts will be available the next day. How many coconuts were available on the first
day.
Farmer
Ray helps raise chickens and cows on his family’s farm. When he looks over
the fence, he counts eight heads, when he looks under the fence; he counts twenty-two legs. Do you think he has more chickens
or cows? How many of each animal does he have?
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