Logic Puzzles

In my geometry class, I can do up to four of these logic puzzles for extra credit (which I NEED). My teacher said that I can get help from my family. So, here they are and you guys (especially Grandma Joan probably) can try to figure them out, and maybe help me out a bit. I think I have the last one figured out, #8. I think it is to ask one of the peoples what the other person will say that they will say. (Like you ask one who happens to be the honest one what the other one will say that they say. So he will say something like "The other one will say that I will say that the other one will say that I will say that...") Does that make sense? If not, help me out.

1. Arrange 12 toothpicks to form six congruent squares. Each square must have one toothpick for each side, and you cannot bend, break, or overlap the toothpicks.
Draw a picture of the figure when you get the answer.

2. Determine the rule for multiplying 11 by any number including 2-digit, 3-digit, and 4-digit numbers.
Show how the rule works on 72, 77, 121, and 1344. I don’t want the product only, I want the procedure explained!

3. King Arthur wants his daughter to marry one of the knights in his kingdom. However, she insists that she be able to marry the smartest knight. She devised a challenge that could be won only by the smartest knight in the kingdom. It went like this:
A dinner party would be held and all the knights in the kingdom would be invited. Only those who wished to take the challenge had to come.
All the knights in attendance would sit around a circular dinner table. King Arthur would start at the head of the table (seat number 1) and go around the circle clock-wise and be-head every other knight until only one was left. The first knight beheaded would be in seat number 2. (Remember, this is a made up story). The one that was left was the smartest knight and he got to marry the King’s daughter.
Here’s the challenge for you to figure out: Not knowing in advance how many knights will show up, how can you determine which seat is the “safe” seat. For example, if 10 knights show up the safe seat is #5. If 25 knights show up the safe seat is #19. If 200 knights show up the safe seat is #145.
To get credit for this problem, determine the safe seat if 7 knights show up, 29 knights, 117 knights, 260, and 550 knights (Do this without a simulation). Show your work. Hint: Simulate the challenge with some small numbers, organize the results, and look for patterns.

4. Each letter in this problem represents a different number between 0 and 9. Find out what number each letter represents.
FOOLELFELF E = ____ F = _____ L = _____ O = _____

5. Using 10 toothpicks, make the following pyramid
........l
.......l l
......l l l
.... l l l l
Move only 3 of the toothpicks to reverse the tower.
..l l l l
...l l l
....l l
.....l
To get credit, show how the toothpicks are moved.

6. A person told a census taker “I have 3 children. The product of their ages is 72 and the sum of their ages is my house number.” The census taker looked at the house number and said, “I still can’t determine their ages.” The person replied, “Oh, I forgot. The oldest one likes chocolate pudding.” The census taker then wrote the children’s ages. What are they and why? (Hint: The person could have said: “Oh, I forgot. The oldest one likes football ( or math or broccoli…etc).”)

7. There were two stairway races. In the first race, the children started at the bottom of the stairs and raced to the top. In the second race, they started at the top and raced to the bottom. The racers were Dameon, Deedee, Ron, Allison, and Kathy.
1. The person who was the last to the top, turned out to be the winner of the race to the bottom.
2. The person who won the race to the top came in third in the race to the bottom.
3. The person who was third to the top was second to the bottom.
4. Kathy was fourth to the top.
5. Allison was fourth to the bottom.
6. Ron reached the top ahead of Deedee.
7. Ron reached the bottom ahead of Dameon.
For each race, tell what order the children finished.
Race to Top Race to Bottom
1st:__________________ 1st___________________
2nd__________________ 2nd___________________
3rd __________________ 3rd___________________
4th __________________ 4th___________________
5th __________________ 5th___________________

8. You are traveling to Truthtown, where everyone always tells the truth. As you are traveling, you encounter a fork in the road. Only one of these roads goes to Truthtown. The other road goes to Badberg, where everyone always lies. A man from one of the cities is standing at the junction. What one question will allow you to determine which road leads to Truthtown?