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

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).