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by ggrrhh_ta
1598 days ago
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The explanation seems to work even in base 10. Let's do the average of 85 and 95.
The leftmost digit of both is equal, so we leave it: X5
The "xor"/2 is the sum of the non equal digits divided by 2 (respecting their powers): (8+9)10 = (17)10 = 85
Now, we add them: 5 + 85 = 90 (which is the average of 85 and 95). Let's take now 87 and 89:
The rightmost digits are equal: 8X
We do the 'xor'/2 for the left most: (7+9)/2 = 8
8X + 8 = 88 Let me know if there are some examples for which it would fail (I only spent a minute to test if the explanation extends to other bases). |
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