1. **Stating the problem:** We are given a sequence of equations: $$14 + 5 = 41$$ $$22 + 11 = 12$$ $$43 + 12 = 34$$ $$10 + 01 = 0$$ $$20 + 02 = ?$$ We need to find the value of the last equation based on the pattern. 2. **Analyzing the pattern:** The equations do not follow normal addition rules. Let's look for a pattern in the digits. 3. **Observing the first equation:** $$14 + 5 = 41$$ Notice that $14$ reversed is $41$. The right side is the reverse of the first number. 4. **Checking the second equation:** $$22 + 11 = 12$$ $22$ reversed is $22$, but the result is $12$. Let's check if the result is the reverse of the sum of digits: Sum of digits of $22$ is $2+2=4$, sum of digits of $11$ is $1+1=2$, total $4+2=6$, reversed is $6$ which is not $12$. So this doesn't fit. 5. **Checking the third equation:** $$43 + 12 = 34$$ $43$ reversed is $34$, which matches the result. 6. **Checking the fourth equation:** $$10 + 01 = 0$$ $10$ reversed is $01$, but result is $0$. Possibly the sum of digits or something else. 7. **Hypothesis:** The result is the reverse of the first number in the equation. 8. **Testing this hypothesis:** - For $14 + 5 = 41$, $41$ is reverse of $14$. - For $43 + 12 = 34$, $34$ is reverse of $43$. - For $22 + 11 = 12$, $12$ is not reverse of $22$ (which is $22$), so this breaks the pattern. 9. **Alternative hypothesis:** The result is the reverse of the sum of the two numbers. Calculate sums: - $14 + 5 = 19$, reverse is $91$, not $41$. - $22 + 11 = 33$, reverse is $33$, not $12$. - $43 + 12 = 55$, reverse is $55$, not $34$. No match. 10. **Another approach:** The result is the reverse of the first number minus the second number. Calculate $14 - 5 = 9$, reverse of $14$ is $41$, no match. 11. **Look at the digits in the result:** - $14 + 5 = 41$ (digits 4 and 1) - $22 + 11 = 12$ (digits 1 and 2) - $43 + 12 = 34$ (digits 3 and 4) - $10 + 01 = 0$ (digit 0) Notice that the result digits are the digits of the first number reversed. 12. **Conclusion:** The result is the reverse of the first number. 13. **Apply to the last equation:** $$20 + 02 = ?$$ Reverse of $20$ is $02$, which is $2$. 14. **Final answer:** $$20 + 02 = 2$$