~~game 4 serious reasoning??~~try this~

priyad

1. Isaac and Albert were excitedly describing the result of the Third Annual International Science Fair Extravaganza in Sweden. There were three contestants, Louis, Rene, and Johannes. Isaac reported that Louis won the fair, while Rene came in second. Albert, on the other hand, reported that Johannes won the fair, while Louis came in second.
In fact, neither Isaac nor Albert had given a correct report of the results of the science fair. Each of them had given one correct statement and one false statement. What was the actual placing of the three contestants?


2. At a family reunion were the following people: one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law. But not as many people attended as it sounds. How many were there, and who were they?


3. 97 baseball teams participate in an annual state tournament. The champion is chosen for this tournament by the usual elimination scheme. That is, the 97 teams are divided into pairs, and the two teams of each pair play against each other. The loser of each pair is eliminated, and the remaining teams are paired up again, etc. How many games must be played to determine a champion?







Solution:
1. Johannes won; Rene came in second; Louis came in third.
2. There were two little girls and a boy, their parents, and their father's parents, totaling seven people.
3. 96. All teams but the champion team will lose a game exactly once.

priyad

1. Three. In the worst case, the first two socks you take out will consist of one black sock and one white sock. The next sock you take out is guaranteed to match one or the other.

2. Two half-full barrels are dumped into one of the empty barrels. Two more half-full barrels are dumped into another one of the empty barrels. This results in nine full barrels, three half-full barrels, and nine empty barrels. Each son gets three full barrels, one half-full barrel, and three empty barrels.

3. $1.19. Three quarters, four dimes, and four pennies.






Solution:

1. Three. In the worst case, the first two socks you take out will consist of one black sock and one white sock. The next sock you take out is guaranteed to match one or the other.
2. Two half-full barrels are dumped into one of the empty barrels. Two more half-full barrels are dumped into another one of the empty barrels. This results in nine full barrels, three half-full barrels, and nine empty barrels. Each son gets three full barrels, one half-full barrel, and three empty barrels.
3. $1.19. Three quarters, four dimes, and four pennies.

priyad

1. A man goes out for a walk. He walks south one mile, east one mile, and north one mile, and ends up in the same place he started. He didn't start out at the north pole -- so where did he?

2. A mountain goat attempts to scale a cliff sixty feet high. Every minute, the goat bounds upward three feet but slips back two. How long does it take for the goat to reach the top?

3. You have three boxes of fruit. One contains just apples, one contains just oranges, and one contains a mixture of both. Each box is labeled -- one says "apples," one says "oranges," and one says "apples and oranges." However, it is known that none of the boxes are labeled correctly. How can you label the boxes correctly if you are only allowed to take and look at just one piece of fruit from just one of the boxes?





Solution:

1. Alternate Solution #1
Assuming a perfectly spherical Earth, somewhere one mile north of the latitude (in the southern hemisphere) that is one mile in circumference. The man walks south one mile to this latitude and walks one mile east, which takes him all the way around and back to where he started. The last step (one mile north) retraces the first step he took (one mile south).
Alternate Solution #2
The man could also be one mile north of the latitude that is one half mile in circumference -- on second leg of the journey, he'd go around twice instead of once. He could also be one mile north of the latitude that is one third of a mile in circumference, or one mile north of the latitude that is one quarter of a mile in circumference, and so on.
2. Fifty eight minutes. Although his net progress each minute is one foot, he reaches the top on the fifty-eighth minute just before he would normally slip back two feet.
3. Take a piece of fruit from the box marked "apples and oranges." Suppose the fruit you take is an apple. Then that box must be the box containing just apples. Therefore, the box marked "oranges" can't be the box containing just apples, and it can't be the box containing just oranges either -- so it must be the box containing apples and oranges. The remaining box is therefore the box containing just oranges.
If the fruit you take out is an orange, the solution is derived in a similar fashion: the box marked "apples and oranges" is the box containing just oranges; the box marked "apples" is the box containing both apples and oranges; and the box marked "oranges" is the one containing just apples.