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Number Code Puzzle

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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?

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Solution Summary

This provides an example of working out a number code.

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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 ...

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