Math 306 - Section 02

Course Information:

Course Syllabus (pdf)
Tentative Course Schedule & Homework Exercises (pdf)

 

TWIX CHALLENGE!

Hungry during our mid-afternoon class? Be one of the first two students to answer the puzzle and get a small treat! There is a new challenge each week.

 

TWIX CHALLENGE #1   In a faraway land there dwelt two groups. The "Group A" were inveterate liars, while "Group B" were unfailingly veracious. Once upon a time a stranger visitied the land, and on meeting a party of three inhabitants inquired to which group they belonged. The first murmured something that the stranger did not catch. The second remarked, "He said he was in Group A." The third said to the second, "You're a liar!" Now the question is, of which group was the third man?  
TWIX CHALLENGE #2   How can you arrange 4 pennies so that there are two (different) straight lines with 3 pennies on each line?  
TWIX CHALLENGE #3   What number is 11 times the sum of its digits?  
TWIX CHALLENGE #4   A bear left its den and went due south in a straight line for one mile. Then it made a 90-degree turn to the left and walked another mile in a straight line. Twice more it made 90-degree turns to the left and walked a mile in a straight line, thus returning to its den. On reaching this starting point, the bear was facing due south. What was the color of the bear? How did you reach your conclusion?  
TWIX CHALLENGE #5   A wooden cube is painted purple on all faces. It is then cut into 27 equal smaller cubes. How many of the smaller cubes are found to be painted on three faces, two faces, one face, and no face?  
TWIX CHALLENGE #6   Your boss wants you to paint a merri-go-round, and the first thing you must do is find out how much paint you need. The center of the merri-go-round is clogged with equipment so you cannot simply measure the inner and outer radii in order to compute the area. After a moment's thought, you exclaim to your boss: ``Ah ha!! I can compute the area (and hence compute the paint needed) with only ONE measurement with my tape measure!'' Your boss, asks: ``How?'' What was your reply to the question? (Remember that a tape measure can only measure the distance between 2 points. No funny business!)