Answers to Puzzles, part 2 Updated February 4, 2000

Solution:

The easy solution is 100 spoons, but since she had to go and buy some of each item... Let x = #plates, y = #spoons, and z = #umbrellas. Okay, because she spent exactly $100, she must have bought a multiple of 20 of the little umbrellas. This leaves: 5x + y + .05z = 100 for z = 20, 40, 60, 80, ... where x + y + z = 100 and x, y, and z are integers. Start at z=20 and solve this set of equation and you'll get z = 80, x = 1, and y = 19.

Solution:

Take one string and light BOTH ends, and light one end of the second string. The first string will burn out completely in 30 minutes. At that time, light the unlit end of the second string. The second string will then burn out in 15 minutes. Total, 45 minutes.

Facts:

1. There are 5 houses in 5 different colours
2. In each house lives a person with a different nationality.
3. These 5 owners drink a certain beverage, smoke a certain brand of cigar and keep a certain pet.
4. No owners have the same pet, smoke the same brand of cigar or drink the same drink.

1. The Brit lives in a red house.
2. The Swede keeps dogs as pets.
3. The Dane drinks tea.
4. The green house is on the left of the white house.
5. The green house owner drinks coffee.
6. The person who smokes Pall Mall rears birds.
7. The owner of the yellow house smokes Dunhill.
8. The man living in the house right in the centre drinks milk.
9. The Norwegian lives in the first house.
10. The man who smokes Blend lives next to the one who keeps cats.
11. The man who keeps horses lives next to the man who smokes Dunhill.
12. The owner who smokes Blue Master drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to the blue house.
15. The man who smokes Blend has a neighbour who drinks water.

Solution:

This puzzle took me a while to solve and is not that easy to explain. First, make a grid, like so:

    1       2       3       4      5
|----------------------------------------
|       |       |       |       |       |  color
|----------------------------------------
|       |       |       |       |       |  country
|----------------------------------------
|       |       |       |       |       |  drink
|----------------------------------------
|       |       |       |       |       |  smoke
|----------------------------------------
|       |       |       |       |       |  pet
|----------------------------------------

#16. From #14 & #9, we know that house #2 is blue. Since from #4, the green house is to the left of the white house, it cannot be house 5 [nothing on its left], or 1 [left of the blue house], so it must be 3 or 4. From #5 & #8, house #4 must be green, so therefore 5 is white, and from #1, 1 is yellow and 3 is red as well as British. We now have all the right colors.

    1       2       3       4      5
|----------------------------------------
|yellow |  blue |  red  | green | white |  color
|----------------------------------------
|norway |       |  uk   |       |       |  country
|----------------------------------------
|       |       | milk  |coffee |       |  drink
|----------------------------------------
|dunhill|       |       |       |       |  smoke
|----------------------------------------
|       |       |       |       |       |  pet
|----------------------------------------

Now for the beverages: We know from #8 that 3 drinks milk, and from #5 and above #16 that 4 drinks coffee. House 1 cannot drink tea because of #3, and cannot drink beer because of #12 and #7 and #16. So house 1 drinks water. Therefore from #15, house 2 smokes Blend and from #11 has a horse and must be Danish [cannot be German who smokes Prince, or Swedish who has a dog]. Thus 2 drinks tea and 5 drinks beer.

    1       2       3       4      5
|----------------------------------------
|yellow |  blue |  red  | green | white |  color
|----------------------------------------
|norway |  dane |  uk   | german| swed  |  country
|----------------------------------------
| water |   tea | milk  |coffee | beer  |  drink
|----------------------------------------
|dunhill| blend |       |prince | blue m|  smoke
|----------------------------------------
|       | horse |       |       |       |  pet
|----------------------------------------

Now 5, who drinks beer and smokes blue master [#12], must be Swedish, so the dog goes here [#2]. House 4 must be German and smokes Prince because house 3 is already British. Thus 3 smokes Pall Mall and owns a bird [#6]. Because of #10, house 1 has a cat. Therefore, the German in house 4 has the fish. Phew.

    1       2       3       4      5
|----------------------------------------
|yellow |  blue |  red  | green | white |  color
|----------------------------------------
|norway |  dane |  uk   | german| swed  |  country
|----------------------------------------
| water |   tea | milk  |coffee | beer  |  drink
|----------------------------------------
|dunhill| blend |  pm   |prince | blue m|  smoke
|----------------------------------------
|  cat  | horse | bird  | FISH! |  dog  |  pet
|----------------------------------------

1. The pilot and copliot are good friends.
2. Shackleford and Colson are not good friends.
3. The engineer's wife is aboard the plane as a passenger.
4. Shackleford and Colson do not wear glasses...
5. ...but I am not sure about the other two guys.
6. Only Garfield and Colson are married.
7. Garfield had lunch with the copilot.
8. The pilot doesn't wear glasses...
9. ...but the navigator does
10. The navigator is engaged to the stewardess.
11. The stewardess is extremely good-looking.

Solution:

This puzzle is considerably easier than the fish one. Still, a grid is helpful: Fill in the obvious clues... #2 4 6 7 & 9

	     Sh       Camp     Garf     Colson 
	|----------------------------------------
friends? | n w/ co |  ---    |         | n w/ sh |
	|----------------------------------------
wife?	|         |         |   yes   |   yes   |
	|----------------------------------------
glasses? |    no   |         |         |    no   |
	|----------------------------------------
job      |         |         | not c/n |         |
	|----------------------------------------

	     Sh       Camp     Garf     Colson 
	|----------------------------------------
friends? | n w/ co |  ---    |  ---    | n w/ sh |
	|----------------------------------------
wife?	|    no   | engaged |   yes   |   yes   |
	|----------------------------------------
glasses? |    no   |   yes   |         |    no   |
	|----------------------------------------
job      | p or co |   nav   | not c/n |   Eng   |
	|----------------------------------------

             Sh       Camp     Garf     Colson 
	|----------------------------------------
friends? | n w/ co |  ---    |  ---    | n w/ sh |
	|----------------------------------------
wife?	|    no   | engaged |   yes   |   yes   |
	|----------------------------------------
glasses? |    no   |   yes   |   no    |    no   |
	|----------------------------------------
job      |    co   |   nav   |  Pilot  |   Eng   |
	|----------------------------------------

1. visual problem
   both descend
2. Street is to curb as river is to ____.
   a. bank b. bed c. dam d. ocean e. stream
   a. bank
3. Size is to grow as knowledge is to ____.
   a. believe b. decide c. know d. learn e. persuade
   d. learn
4. Canyon is to bridge as mountain is to ____.
   a. cave b. mine c. peak d. ridge e. tunnel
   e. tunnel
5. Water droplet is to air bubble as island is to ____.
   a. bay b. continent c. crater d. lake e. peninsula
   d. lake
6. Mountain is to pyramid as river is to ____.
   a. bathtub b. canal c. fountain d. reservoir e. well
   b. canal
7. Water is to stalactite as wind is to ____.
   a. dune b. geyser c. skyscrapper d. stalagmite e. volcano
   a. dune
8. What number best completes the sequence?
   1000, 1002, 1006, 1012, 1020, ____.
   1030 [+2 +4 +6 +8 +10]
9. What number best completes the sequence?
   13, 57, 911, 1315, 1719, ____.
   2123 [made up of the next 2 odd numbers]
10. One (infinite) line can divide an (infinite) plane into two regions. Two distinct line can divide a plane into 3 or 4 distinct regions. How many regions can 3 distinct lines divide a plane into?
    4, 6, or 7
11. The cities Weston and Easton are connected by parallel eastbound and westbound railroad tracks. Trains run daily on a 24-hr basis. Trains depart Weston for Easton every hour on the hour (i.e., at 6.00, 7.00, etc). Trains depart Easton for Weston on the half hour (i.e., 6.30, 7.30, etc). In either direction, the trip takes 6 hours. If you take a train from Weston to Easton, how many trains do you pass on the way?
    12
12. If bond equals 1.10.3.2 and market equals 7.6.8.1.5.9, then bank equals _____.
    4.6.3.1
13. What does 1000 - 999 + 998 - 997 +... + 4 - 3 +2 -1 =?
    500
14. A couple plans to have three children. If the odds of having a girl is exactly the same as the odds of having a boy (1 in 2), then what are the odds of have all three children of the same sex?
    2 x 1/8 = 1/4

In ancient Greece, when the Gods ruled the world, Iganor, the God of bad luck, sentenced a mortal warrior to death. Iganor was a reasonable God and allowed the warrior to choose his method of death. The warrior was allowed to make one statement; if the statement were true, the warrior would be fed to the dragons and if the statement were false, the warrior was to be killed by a poisoned fruit tart!

The warrior mulled his predicament over and finally made a statement. After hearing it, Iganor had no choice but to free the warrior. What did the warrior say to save himself?

Solution:

Essentially, he needs to contradict Iganor's terms witha paradox. He can say, "I will be killed by a poison fruit tart," or, "I will not be fed to the dragons."

A boat leaves a pier and travels UPSTREAM [ie, against the river current] for one mile. There, it passes a log floating on the river heading [obviously] downstream. The boat then keeps traveling for one hour; then turns around and heads back toward the pier where it came from. The boat and the log arrive at the pier simultaneously. Assume that the boat is traveling at a constant engine speed, and that the river is also flowing at a constant speed.

How fast is the boat going? What about the river?

Solution: The answers are: the river is flowing at ?miles per hour, while it does not matter how fast the boat is moving, as long as it exceeds ?miles per hour. Let's set up the solution:

(P)___1 mile___(q)___________(x-y)____________

(P)= pier
(q)= where the boat first spots the log
 x = the neutral speed of the boat
 y = the speed of the river, and therefore the log

The boat first travels 1 mile. It then travels for one more hour. Upstream, 
its speed would be (x-y) so it travels (x-y) miles. During the time the boat 
travels that (x-y) distance upstream, the log travels downstream at a speed of y, 
so it would have moved y miles so is now (1-y) miles away from the pier. Now, 
the boat & log will take the same time to travel (1 + x - y) and (1 - y) miles 
respectively. Note that the boat will now travel at x + y miles per hour as 
it is traveling upstream.

So:

(1 + x - y)      (1 - y)
-----------  =   -------
  (x + y)           y

y + xy - y^2 = x - xy + y -y^2

x= 2xy
y= ?
The reason why it doesn't matter what speed the boat is travelling at 
is because this factor gets canceled out on the return trip. That is, 
whatever that boat speed is going out, will be the same going back.

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