|
PUZZLE PAGE 3
***************************************
Sorry No August Puzzle
Please come back 09/01/2003
***************************************
Puzzle #53 07/01/2003
The above graphic shows a chessboard that has had its upper left square
and its lower right square "sawed off". Underneath that is a domino that
is exactly the size of 2 of the chessboard squares. If you had 31 of these
dominoes, would you be able to arrange them so that ALL 62 squares
were covered ?
ANSWER
31 dominoes could NOT cover the chessboard completely and the proof
is quite simple. Each domino must cover a white square and a black
square. However, the chessbord has had 2 corner squares removed -
and they are both white. Therefore, it cannot be done.
***************************************
Puzzle #52 06/01/2003
Let's assume that a $20 gold piece weighs twice as much as a $10 gold
piece. So, which would you rather have, a half pound of $20 gold pieces
or a pound of $10 gold pieces?
ANSWER
At first glance this seems to be similar to that old puzzle -
"what's heavier - a pound of feathers or a pound of lead?" And the
answer is they are the same thing.
However, this is a twist on that old puzzle. Let's suppose (to keep things
simple) that a $10 gold piece weighs an ounce and a $20 gold piece
weighs 2 ounces. So a half pound (8 ounces) of $20 gold pieces is 4
coins equalling $80. A pound (16 ounces) of $10 gold pieces is 16
coins totalling $160.
Basically, this puzzle is asking, "would you rather have a half pound of
gold or a pound of gold?"
***************************************
Puzzle #51 05/01/2003
An airplane pilot overheard a woman say that she had missed her flight. The
pilot said "I can give you a ride and I'll charge you nothing because you won't
even be taking me out of my way." The woman was very suspicious of this offer
especially when she said "But you don't even know where I'm going !!" The pilot
said "It doesn't matter. It will not be out of my way." The pilot was not lying so
just where the heck was he going?
ANSWER
He was going to the opposite side of the Earth. For example, if he were
in Honolulu, Hawaii he was headed for Mozambique, Africa.
On the surface of the Earth, the shortest distance between 2 points is
a "great circle route". So, when you are traveling to the exact opposite
side of the Earth, there are an infinite number of great circle routes you
can choose and one of which would take you over the destination
where the woman wanted to go.
Granted, in reality it would be difficult to fly ANY great circle route you
chose. You have to consider places for refueling. There are
many places that have restricted airspace and some countries would not
allow you to have ANY air rights whatsoever. Then the weather of a
particular region might make things difficult if not dangerous. (Flying
over Antarctica in the dead of winter, for example).
STILL, it does make an interesting puzzle doesn't it?
***************************************
Sorry, NO April Puzzle - Come Back In May
***************************************
Puzzle #50 3/1/2003
How about an easy puzzle this month? A class consists of 58% girls and
42% boys. There are 6 more girls than boys in the class. How many
TOTAL students are there?
ANSWER
We can set up 2 equations:
.58*g = .42*b + 6
g = b + 6
Substituting the second equation into the first we get:
.58b + 3.48 = .42b + 6
.16b = 2.52
b = 15.75
Since we can't have decimal portions of people, we can truncate it to 15.
So, there are 15 boys and 21 girls for a total of 36 students.
Due to rounding of the percentages there are two more answers.
16 boys + 22 girls = 38 students and 17 boys + 23 girls = 40 students
So, all three answers are correct !!!
***************************************
Puzzle #49 2/1/2003
This puzzle involves similar probability principles as Puzzle #48. Instead of rolling
2 dice, let's say you are flipping 2 coins. There are 4 possible
outcomes for each flip of the 2 coins:
"Head, Head"; "Head,Tail"; "Tail,Head"; "Tail,Tail"
Again you reason that since 2 Heads is 1 of the 4 combinations, then flipping
2 coins twice will give you a "50/50" chance of getting 2 heads at least
once.
Is this reasoning correct ?
ANSWER
This is not a good bet either. There are 4 possible outcomes of one flip of
two coins and so there are 16 possible outcomes of 2 flips:
1st Outcome 2nd Outcome Successful ?
1) H H H H Y
2) H H H T Y
3) H H T H Y
4) H H T T Y
5) H T H H Y
6) T H H H Y
7) T T H H Y
8) H T H T N
9) H T T H N
10) T H T H N
11) T H H T N
12) T T H T N
13) T T T H N
14) T H T T N
15) H T T T N
16) T T T T N
Notice that the successful outcomes are only 7 out of 16 and not 8 out of
16. (Note: Case #1 is considered only 1 success - not two). Therefore, you
will only be successful 43.75% of the time and not 50%.
If you still doubt the reasoning of this, try flipping 2 coins
yourself OR write a computer program to simulate this. Even the RAND()
function in MS Excel™ will allow you to run such a simulation.
***************************************
Puzzle #48 1/1/2003
When rolling 2 six-sided dice, there are 36 possible combinations. Out
of these 36 combinations, there is only one way that a twelve (2 sixes) can
appear.
You are offered an even-money bet (let's say for $10) that if you can
throw a twelve in 21 throws, you win $10. If not, you lose $10. Also, you
may continue to make bets for as long as you'd like.
You reason that a twelve is 1 out of the 36 dice combinations, therefore
your chances are 50-50 after 18 rolls and with 21 tries you are going to
come out a winner more often than not. Is this reasoning correct?
ANSWER
Actually, the answer is quite complex and involves the binomial distribution
theorem. To calculate the odds, you would have to determine all possible
outcomes for each roll of the dice and then determine which of
those are "successes". For any number of throws of the dice (or 'n'), all
possible outcomes equal 36n. So, for example, after 10 throws of
the dice, the number of all possible outcomes = 3610 =
3,656,158,440,062,980. Then you would have to calculate the successes. Suffice
it to say that these calculations would take up a lot of page space.
Fortunately, the calculations have already been done. The odds are slightly
against you after 24 throws and only turn in your favor after 25 throws. So,
taking this bet would not be a good idea. In fact in 1952, a gambler
named "Fat the Butch", agreed to this bet (except at $1,000 for 21 rolls).
After losing $49,000 he realized that something had to be wrong with his
reasoning. Use a search engine to find out more about this.
|