1999 TRINITY MATH TRIATHLON

1.   A twenty-four hour digital clock displays the correct time on January 1, 1999 at noon.  If the clock loses 15 minutes per day, what will be the next date when the clock displays the correct time?

2.  A sheet of paper is yellow on one side and blue on the reverse side.  The lower right corner is folded to the left side of the paper so that the resulting figure is a yellow rectangle above a blue triangle.  What is the area of the sheet of paper, if the width of the paper is 10 cm. and equal areas of blue and yellow appear after the folding?

3.  Suppose that n# means 1/n, the reciprocal of n.  For example 5# means 1/5.  Classify each of the following as true or false.

a.   2#  × 6# = 12#
b.   3# + 6# = 12#   + 3#
c. 10#  ÷ 2# = 5#
d. (0.4)# - (2/3)# = 1#
e. [(3#)#  + (2#)#]#=5#

4.  In a classroom, one of four students-Adam, Beth, Cathy, and Dan-draws a picture on the chalkboard.  When the teacher enters, she asks who drew it.  Cathy says "Adam did it."  Beth says "Cathy did it." Adam says "Cathy lied when she said that I did it." Dan says "I didn't do it."  If only one of the students is telling the truth, then who drew the picture?

5.  Replace the letters with a distinct digit in this addition exercise:
 

	EINS (German for "one")
	EINS
	EINS
+	EINS
	VIER (German for "four")