11/2003

##### To talk goodness is not good...Only to do it is.  - Chinese Proverb

Theory

Number Base Systems

 Decimal Binary Ternary Oct. Hex. 0 0 0 0 0 1 1 1 1 1 2 10 2 2 2 3 11 10 3 3 4 100 11 4 4 5 101 12 5 5 6 110 20 6 6 7 111 21 7 7 8 1000 22 10 8 9 1001 100 11 9 10 1010 101 12 A 11 1011 102 13 B 12 1100 110 14 C 13 1101 111 15 D 14 1110 112 16 E 15 1111 120 17 F 16 10000 121 20 10 17 10001 122 21 11 18 10010 200 22 12 19 10011 201 23 13 20 10100 202 24 14
##### Solutions from the Previous Issue:

Find y from the following equations:

1. y3 = 27

Solution: y3 = 27; y=3

1. (–2)3 • 2y • 2-7 = -1

Solution: (–2)3 • 2y • 2-7 = -1; 3 + y - 7= 0; y – 4 = 0; y = 4;

Simplify:

Solution: = =

1. (4x3)2

Solution: (4x3) 2 = 16x6

Solution: =

## Proposed Exercises:

1. How many different coin combinations could a person have if she has exactly 21 cents?
2. In the movie Tandem, a character explains that the number on his car's odometer, 83238, is a palindrome, since it reads the same from left to right as from right to left. He then remarks that the next palindrome will be 83338. What number is the seventh palindrome after 83338?
3. The pattern AABBBCCCCAABBBCCCC continuously repeats. What is the 2003rd letter in the pattern?
4. Without using a calculator or computer, determine which is larger, 23000 or 32000.
5. If a and b are positive integers, neither of which is divisible by 10, and if ab = 10,000, find the sum a + b.