# Number Code Puzzle

4. An AE student named Seoung devises a coded system of arithmetic for keeping his financial information private. His coded system of arithmetic is identical to the usual one except that each digit 0 to 9 has a value different than from standard arithmetic.

The following five equations hold in Seoung's arithmetic:

(a) 8×7 = 8

(b) 4×9 = 39

(c) 7-33 = -1

(d) 51÷2 = 2

(e) 7^4 = 6.

What is the sum 40 + 04 in Seoung's arithmetic expressed in his new digits?

https://brainmass.com/math/discrete-math/number-code-puzzle-228875

#### Solution Preview

I break it as follows.

8 --> 0

7 --> 2

3 --> 1

1 --> 9

5 --> 4

2 --> 7

4 --> 3

6 --> 8

9 --> 5

0 --> 6

Thus 40 + 04 = 46 + 64 = 110

The answer is 110.

How to decode?

Step 1: From (a), 8x7 = 8, and (c) 7-33 = -1, we first know that 7 can not be 0. If 7 is 0, 7-33 should be two digits, not -1.

So 8 has to be 0 or 1. But from (c), 3 has to be 1 ...

#### Solution Summary

This provides an example of working out a number code.