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FUZZY MATH
EASY:
A in five hours a sum can count,
Which B can in eleven j
How much more then is the amount
They both can count in seven?
If a man 6 feet high could walk around the earth on
the equator, how much farther would the top of his head
move than his feet?
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MEDIUM:
I own a lot located in the wealthiest section
of New York City and am desirous of knowing its exact area.
The dimensions according to the deed are exactly 101 rods,
51.5 rods and 49.5 rods respectively.
I guarantee to have just what the deed calls for and wishing
to share my wealth with friends have decided to reward
each of the first 99 sending in correct solutions showing the
exact area of the tract with a .01 interest in the land. You
are only asked to pay the cost of the deed. What is the
area?
A miner asks for room and board at a hotel for fifty
days. He is told that the price is $1 a day. He has no
money, but he has a heavy gold chain with fifty links, each
worth a dollar. He agrees with the landlord to cut the chain
and pay one link each day. At the end of fifty days the
miner will redeem the chain and have it soldered together.
The miner does not wish to cut the chain any more tha n
is necessary. How many links will it be absolutely necessary
for him to cut?
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MAGICAL:
The number nine possesses the most remarkable properties
of any of the numbers 1 , 2, 3, 4, 5, 6, 7, 8, and 9.
Many of these properties have been known for centuries
and have excited much interest among both mathematicians
and scholars in general. Because of its wonderful properties
the number nine has been regarded as magical and is often
referred to as the ” magical number. ”
If we were using the duodecimal scale to-day instead of
the decimal, to what number would all the properties of the
number nine belong?
PROPERTIES OF NUMBER NINE
Some of the properties of the ” magic ” number 9 are
as follows :
(a) The sum of the digits of any number which is a multiple
of 9 is either 9 or a multiple of 9. Thus,
l X 9 = 9
2 X 9 = 18
3 X 9 = 27
4 X 9 = 36
5 X 9 = 45
6 X 9 = 54
9 = 9
1 +8 = 9
2 + 7 = 9
3 +6 = 9
4 + 5 = 9
5 + 4 = 9
7 X 9 = 63
8 X 9 = 72
9 X 9 = 81
10 X 9 = OO
11 X 9 = 99
12 X 9 = 108
435 X 9 = 3915.
6 + 3 = 9
7 + 2 = 9
8 + 1 = 9
9 + 0 = 9
9 +9 = 18 = 1 + 8 = 9
1 +0 + 8 = 9
3915 = 3 + 9 + 1 + 5 = 1 8 = 1 + 8 = 9.
This is true for every multiple of 9 . When we have the
factor 9 in a number, it will cling to the expression and will
appear at unexpected times and in a variety of ways. This
is because of its relation to the numerical scale. Whatever
you do, the figure 9 is sure to turn up again. It is impossible
to get rid of it.
(b) If you take a number consisting of any number of digits
and change their order as you please, the number thus obtained
for any arrangement of digits, when divided by 9, will leave the
same remainder.
Thus 2345, 3245, 5234, etc. when divided by 9 in each
case gives the same remainder, 5. This follows because
the sum of the digits is the same for every arrangement.
The remainder from dividing a number by 9 is the same as
the remainder from dividing the sum of its digits by 9.
(c) Take a number consisting of any number of digits.
Form a new number by reversing the order of the digits. The
difference is always divisible by 9.
(d) Take the sum of the digits from any number and the
difference will be divisible by 9.
(e) Take two numbers in which the sums of the digits are the
same, the difference of the two numbers will be divisible by 9.
