An erroneous subtraction shows 789 - 456 = 123. It can be corrected by 3 pairs of digit interchanges (7, 3), (3, 4), and (9, 6). Can you correct it in 2?

#### The Riddle

A problem of subtracting 456 from 789 shows an erroneous result of 123. This error in the subtraction can be corrected by three digit interchanges in sequence: (7 and 3), (3 and 4), and (9 and 6) converting it to (486 - 359 = 127). But can you achieve a correct result with just two interchanges?

**Recommended time to solve:** 6 minutes.

To solve this riddle efficiently, it’s essential to approach it strategically. You may lose your way in random attempts unless you focus on identifying the right goals and apply simple mathematical reasoning based on the hidden patterns within the numbers.

### Solution to Subtraction Riddle Challenge: Fix the Error with Only Two Interchanges

#### Step 1: Understand What the Three Interchange Solution Tells Us

The solution with three digit interchanges simply indicates that *interchanges between all three numbers involved in the subtraction are allowed.*

This being the only certain new information, rather than analyzing this solution's mechanism in depth, let’s focus on solving the puzzle with only two interchanges.

#### Step 2: Identify the Right Goal and Define the Strategy

Our objective is to use the minimum number of interchanges for the solution. This translates effectively to:

**Right Goal:**Maximize the number of digits left undisturbed.

The right strategy to meet the goal is then:

**Strategy:**Identify the maximum number of digits already in their right places in the incorrect subtraction.

#### Step 3: Identify the Digits Already in Their Correct Places

**First Key Insight**

- The units digits are already correct: 9 - 6 = 3.

**Conclusion based on common-sense reasoning:**

Units digits should be left undisturbed.

With this assumption, **the puzzle simplifies to:**

Correct the subtraction (78 - 45) = 12 by interchanging two pairs of digits.

It follows:

**Reasoning:**If two pairs of digits are to be interchanged out of six in the simplified puzzle, two digits must remain in their original positions.

#### Step 4: Discovering the Crucial Pattern for Solution

Original erroneous subtraction:

- 7 8 9 - 4 5 6 = 1 2 3

Simplified erroneous subtraction:

- 7 8 - 4 5 = 1 2

It takes no time to identify the patterns in the four digits crucial for the final solution:

- (7 - 5) = 1, with a borrow of 1 from the right.
- (2 - 8) = 4, creating a borrow to the left.

Applying the Insight for the Solution:

**First interchange: 4 and 5:**

7 8 9 – 5 4 6 = 1 2 3

**Second interchange: 2 and 8:**

7 2 9 – 5 4 6 = 1 8 3

Not so difficult, isn't it?

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