If 54 + 43 = 2 and 60 + 51 = 10 by a special rule, then what is the value of 62 + 72 under the same rule?

Introduction / Context:
These puzzles often redefine "+" by a hidden rule, frequently using digit operations. We must infer the rule that makes the sample equalities true.

Given Data / Assumptions:

• 54 + 43 = 2
• 60 + 51 = 10
• Find 62 + 72.

Concept / Approach:
Consider sum of absolute differences of corresponding digits: (tens difference) + (ones difference). This fits both examples elegantly.

Step-by-Step Solution:
For 54 and 43: |5-4| + |4-3| = 1 + 1 = 2.For 60 and 51: |6-5| + |0-1| = 1 + 1 = 2, which does not match 10. Try digit-wise difference without absolute value but multiplication by position? Another simple pattern is (tens difference)* (ones difference): (5-4)*(4-3)=1*1=1, not 2. A more consistent fit is to sum differences separately as (5-0) + (4-? )? Instead, observe another valid rule: sum of digit differences across cross-pairs: |5-1| + |4-0| = 4 + 4 = 8, still not 10. Now notice a better consistent rule: (first tens - first ones) + (second tens - second ones). For 54, 43: (5-4)+(4-3)=1+1=2. For 60, 51: (6-0)+(5-1)=6+4=10, which matches.Apply to 62 and 72: (6-2)+(7-2)=4+5=9.

Verification / Alternative check:
This rule matches both given examples exactly and yields a unique answer for the query pair.

Why Other Options Are Wrong:

• 30 / 18 / 20: do not follow from the established digit-difference rule.
• None of these: Not necessary since 9 is obtained consistently.

Common Pitfalls:
Using absolute sums of digit differences in the same places, which fails for 60 and 51.

Final Answer:
9