Group Name: Names of Group Members: ______

Math Club Worksheet #19

These brain Brain twisters are fun and challenging. Use common sense, and don’t be afraid to think outside the box!

Problems: Work with your group to use your math and thinking skills to solve these problems. Don’t worry if you can’t solve all of them immediately, especially the bonus questions.

1. In this puzzle you must help a farmer get a fox, a chicken, and a bag of corn safely across a river in a boat. The farmer may only take one thing at a time in the boat. She cannot leave the fox and the chicken together on either side of the river, or the fox will eat the chicken. Likewise, she cannot leave the chicken alone with the bag of corn or the chicken will eat the corn. How can the farmer get everything across the river without anything being eaten?

2. In a country there live 'knights' and 'knaves.' The 'knaves' always lie and the 'knights' always tell the truth - unless they make a mistake. 1995 knights and knaves are sitting around a table. Each says that he is sitting between a knight and a knave, but two knights are mistaken. How many knaves are seated at the table?

3. Three men pay $10 each for a $30 hotel room. Later, they receive a $5 refund. Because they cannot easily split the $5, they each keep $1 and give the bellboy a $2 tip. Thus, each man's share of the room is $9. The $9 multiplied by three is $27. When the $2 tip is added the total is $29. The conundrum comes in determining what happened to the missing dollar. 4. A firefighter and a carpenter are standing in line to go to a movie. One of them is the father of the other one’s son. How is this possible?

5. What is the maximum and minimum number of pieces of pie possible after 3 straight cuts?

6. The first challenge in this puzzle is to draw in lines on the clock face below so that the face is divided into three regions in such a way that the sum of the numbers in each region is the same. The second challenge is similar to the first. This time the lines you draw must divide the clock face into six regions. Again, the numbers in each region must have the same sum.

7. Thirteen teachers are in Paradox, New York attending a math conference. When they arrive at the Enigma Hotel to check in, they are told that only 12 rooms are available. Since their school had made reservations for 13 rooms, the teachers are a bit upset that they will have to find another place to stay. As they are preparing to leave and find another hotel, the manager comes out and asks if there is a problem. When she hears of their situation she assures them that the Enigma Hotel has enough space to accommodate each teacher in his or her own room. She takes two of the teachers to room #1 and promises to come back in a few minutes and take one of them to another room. She takes the third teacher to room #2, the fourth teacher to room #3, the fifth teacher to room #4 and so on, taking the twelfth teacher to room #11. She then returns to room #1 and escorts the extra teacher waiting there to room #12. All of the teachers are now happily settled in their own rooms. Is this possible? Why or why not?