1. The problem involves a custom operation $ \oplus $ defined on numbers arranged in a circular clock-like diagram with numbers from 0 to 7. 2. Given examples are: - $3 \oplus 2 = 5$ - $4 \oplus 5 = 1$ - $6 \oplus 1 \oplus 3 = 2$ 3. We need to understand the operation $ \oplus $. Observing the examples, it appears that $ \oplus $ corresponds to addition modulo 8, since the numbers wrap around after 7. 4. The formula for addition modulo 8 is: $$a \oplus b = (a + b) \bmod 8$$ 5. Let's verify the examples: - $3 \oplus 2 = (3 + 2) \bmod 8 = 5$ - $4 \oplus 5 = (4 + 5) \bmod 8 = 9 \bmod 8 = 1$ - $6 \oplus 1 \oplus 3 = ((6 + 1) \bmod 8 + 3) \bmod 8 = (7 + 3) \bmod 8 = 10 \bmod 8 = 2$ 6. Therefore, the operation $ \oplus $ is addition modulo 8 on the numbers arranged in the circle. 7. This means to compute $a \oplus b$, add $a$ and $b$ and then take the remainder when divided by 8. Final answer: $a \oplus b = (a + b) \bmod 8$