Math Quiz Four

MathQuiz 4 is easy. But don't answer if you stink in math.

 0 points - Wrong answer
 1 point - Right answer
 2 points - Right answer with explanation

There are Four (One just added) questions.

Email me at HapAngery@netscape.net to answer them. Changed

1. Five men and a monkey were lost in a jungle. They spent the first night gathering bananas. They piled them together and went to sleep. When they all were asleep, one man woke up, and thinking there might be a row about dividing the bananas, he decided to take his share. First, he gave one banana to the monkey, and then he divided the rest of the bananas into five equal piles. He took one pile, and put the rest back together. By and by, the next man woke up and did the same thing. He gave one banana to the monkey and divided the bananas into five equal piles and took one pile. in turn, each of the remaining three men men did the same thing, each giving the monkey one banana first and then taking 1/5 of the remaining bananas. In the morning, the five men divided what bananas they had left into five equal shares, each taking one share. Of course, each of the men knew there were bananas missing, but no-one said anything. What is the least amount of bananas they could have in the pile before anyone took any? [Adapted from MartinGardner's column in ScientificAmerican.]

2. A rotating barber's pole consists of a cylinder on which red, white, blue helices are painted. The cylinder is four feet high. The red stripe cuts the cylinder's elements (vertical lines) with a constant angle of 60 degrees. How long is the red stripe?

3. A grocer is displaying oranges in two tetrahedral pyramids. By using all the oranges in both pyramids, he is able to make one large tetrahedral pyramid. The smallest number of oranges he can have, if the two small pyramids are the same size, is 20. If they are different sizes, what is the smallest number of oranges he can have?

4. Find the basis for the arrangement below

       8 5 4 9 1 7 6 8 2 0 

Are parts 2 and 3 also from ScientificAmerican?

They came from a book called Colossal Book of Mathematics, by MartinGardner {ISBN 0393020231 }, which is an updated collection of his articles in ScientificAmerican.

Q1: 3121 bananas - a simple computer program suffices to confirm this answer by trial and error, or proceed as described in Scientific American.

Q2: 8 feet (ignoring measurement difficulties due to the width of the stripe), due to a right-angled triangle with angle specified being half of an equilateral triangle.

Q3: 690 (570 + 120), again verifiable by trial and error. A better method doesn't seem to be readily available, which makes this a very poor type of question. -- VickiKerr

Question 1 and 2 are right. Question 3 is wrong, try new calculations. Vey One sorry -- HapAngery

Oops! While waiting for your email address to be corrected, I lost my original notes. In recreating my last answer, I inadvertently added in 10 incorrectly. I should have given 680 (560 + 120). -- VickiKerr

Q4: Alphabetical order of the English names for the digits.

Wrong, look closely, it's not, got tricked. -- HapAngery

Not at all - you changed "3" to "8" in the question after it was correctly answered. Alphabetical order is still the basis, even if one digit doesn't fit the overall pattern.

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Here's a horrible PythonLanguage program I wrote to figure out the bananas question. I initially emailed it to the incorrect email address but now that the answer is out I figured I'd post it here. -- BrianRobinson

def man(x):

    stop = "no"
    x -= 1           #one for the monkey
    if x % 5 != 0:   # five equal piles
        stop = "yes"
    elif  x / 5 < 1: # each man gets at least one
        stop = "yes"        
    else:
        x -= x / 5
    return x, stop

def finalSplit(x):

    correct = 1
    if x % 5 != 0:   # five equal piles
        correct = 0
    elif  x / 5 < 1: # each man gets at least one
        correct = 0
    return correct

for bananas in range(1000000):

    temp = bananas
    for men in range(5): # five men
        temp, stop = man(temp)
        if stop == "yes":
            stop = "no"
            break
        stop = "good"
    if stop == "good" and finalSplit(temp):
        print bananas
        break

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But everyone knows the answer to problem 1 is -4. Solve x = 4/5(x-1). For a better answer, realize that any true answer must be equivalent to -4 modulo 5^5. And 5^5 - 4 is 3121. -- EricJablow

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CategoryMath