January 2002 TRINITY MATH TRIATHLON

1.  Let $ denote a binary operation defined by: 

a. Find 5$4. 
b. Find (4$2)$3. 
c. Find x if x$y=28 and y=5.
d. True or False:  8$2=-2$-3. 
e. True or False: 

2.  Draw 2 squares in the diagram so that all the stars are separated.

3.   Consider a set of small boxes each of dimension 2×2×3.  Find each of the following:

a. What is the largest number of the small boxes that can be placed inside a box of size 3×4×5?
b. Find the minimum surface area of a box that will contain 9 of the small boxes.

4.  Consider 10 numbers represented by A, B, C, D, E, F, G, H, I, and J where  A < B < C < . . . < I < J.  You know the following things about the numbers:
 

(1) The average of the numbers is 30  (2) F = 33  (3) J = 10 * A  (4) D = A2  (5) A + D + J = 80 (6) I = J - 3

(7) There are four prime numbers (8) The average of the prime numbers is 24 (9) B and E are prime numbers (10) H = C + 18 (11) G is 2 more than the average of the composite (non-prime) numbers

What are the numbers?

5.  Find two ways in which you can replace the given letters with distinct digits from 1 to 9  (inclusive) in this addition exercise:
 

	Z W E I  (German for "two")
+	Z W E I
	V I E R  (German for "four")