For
second month, no Math Puzzler winners
The Math Puzzler
questions in November were too tough for all entrants. This
was the second month in a row that no one was able to answer
all of the six questions correctly.
Before that, there
had been winners for several months in a row.
But, it looks
like the December Math Puzzlers might provide a chance for
contestants to return to winning ways. Many of the December
questions are similar to previous questions.
That means that
by looking back to past Math Puzzlers, you'll find answers
to those previous "close cousins" questions.
Mr. Math Puzzler
started giving math questions in September, 2001. That means
there are over two years of questions--and answers--to review.
Just go to the
Past Stories tab on the home page. Behind that, there
are over two years of past Puzzlers. Click on the "answers"
story for both the questions and explanations of the answers.
One way to review
would be to print out the December, 2003, questions and then
look for similar ones in past Puzzlers. The past answers always
have an explanation of how to arrive at the answer.
Remember, if any
contestant gets all six answers correct, we publish their
names in the following month. That's also the time when we
give the explanations for the previous month's questions.
Also, as an added
incentive, we enter all kids who get six right answers into
a drawing for $10 Border's book certificates. Up to three
certificates will be awarded each month.
The
November Math Puzzler answers
1. Let us follow
the hour hand and minute hand of a clock for 24 hours. How
many times do the hands form a right angle during that period?
Answer:
44
The explanation:
The minute and hour hands cover each other 12 times in a 12-hour
period. That means there are 11 time segments in each hour
and two times each hour the hands are at right (90 degree)
angles. Thus, 11 times 2 equals 22. Then, for 24 hours, that
would be doubled, or 44.
2. Add arithmetical
symbols in the spaces between the 4's to make each equation
true. Remember, you may use parentheses also.
- 4 _ 4 _ 4
_ 4 = 3
- 4 _ 4 _ 4 _
4 = 6
- 4 _ 4 _ 4 _
4 = 7
- 4 _ 4 _ 4 _
4 = 8
- 4 _ 4 _ 4 _
4 = 24
- 4 _ 4 _ 4 _
4 = 28
- 4 _ 4 _ 4 _
4 = 32
- 4 _ 4 _ 4
_ 4 = 48
Answer:
See below
The explanation:
- [(4 x 4)
- 4] divided by 4 = 3
- (4 + 4)
divided by 4 + 4 = 6
- (4 + 4)
- (4 divided by 4) = 7
- (4 x 4)
- 4 - 4 = 8
- 4 x 4 +
4 + 4 = 24
- (4 + 4)
x 4 - 4 = 28
- (4 x 4)
+ (4 x 4) = 32
- (4 + 4
+ 4) x 4 = 48
3. If 73 hens
lay 73 dozen eggs in 73 days and if 37 hens eat 37 kilograms
of grain in 37 days, what weight of grain corresponds to one
dozen eggs?
Answer:
73/37 kilograms
The explanation:
We'll set up a graph to show the possibilities:
| Hens |
Dozen
Eggs |
Days |
Kg of
wheat |
| 73 |
73 |
73 |
-- |
| 37 |
-- |
37 |
37 |
Thus 73 hens
will produce 1 dozen eggs in 1 day
And 37 hens will eat 1 kilogram of wheat in 1 day
Thus, one dozen eggs will be produced by 73/37 kilograms of
wheat
4. In a certain
town with 100 men, 85 are married, 70 have a telephone, 75
own a car and 80 own a house. What is the least possible number
of men who are married, have a phone, own a car and own their
own house?
Answer:
10 men
The explanation:
Of the 100 men, 15 aren't married; of the 100 men, 30 don't
have a phone; of the 100 men, 25 don't own a car, and, of
the 100 men, 20 don't own a house. That means there are 90
men who don't have at least one of the criteria. That means
10 men must have them all.
5. The same two
numbers are added on the left and subtracted on the right.
Each variable represents a different digit. That is, if A
= 3, then B can't = 3. Find all the digits.
X
Y Z X Y Z
+ A B
- A B
------- -------
C D E F B
G A
Answer:
See below
The explanation:
You start the logic of this answer by assuming the X is 9
(That's because in the first example, you know that C must
be 1, since there are four digits in the answer but only three
digits in the top number. Using similar logic, the answers
will turn out to be:
945
945
+ 78
- 78
---- ----
1023
867
6. Replace each
star (*) with a digit to make the equation true.
***, 4** X 7
= 6,743,*56
Answer:
963,408 x 7 = 6,743,856
The explanation:
This is another answer that is arrived at by logic. For instance,
the only way the answer can end in 56 is for the last two
*s in the first number must be 0 and 8. Then, multiplying
408 by 7 fills in the only * in the answer as 8. The rest
of the answer flows logically once you get that far.
