If we increase each even digit by "1" and decrease each odd digit by "1" in the number "7846921453" and then arrange all the number in descending order, then what is the sum of the last five digits from the right end after the rearrangement?
35
Digit Transformation and Sum Calculation
Follow these steps to find the required sum:
Step 1: Apply Digit Transformations
Modify each digit in the number "7846921453" based on the rules: increase even digits by 1 and decrease odd digits by 1.
- 7 (odd) becomes 7 - 1 = 6
- 8 (even) becomes 8 + 1 = 9
- 4 (even) becomes 4 + 1 = 5
- 6 (even) becomes 6 + 1 = 7
- 9 (odd) becomes 9 - 1 = 8
- 2 (even) becomes 2 + 1 = 3
- 1 (odd) becomes 1 - 1 = 0
- 4 (even) becomes 4 + 1 = 5
- 5 (odd) becomes 5 - 1 = 4
- 3 (odd) becomes 3 - 1 = 2
The transformed digits are: 6, 9, 5, 7, 8, 3, 0, 5, 4, 2.
Step 2: Arrange Digits in Descending Order
Sort the transformed digits from largest to smallest (descending order):
9, 8, 7, 6, 5, 5, 4, 3, 2, 0
Step 3: Identify the Last Five Digits (from the right end)
In a descending sequence, the "last five digits from the right end" refers to the five largest digits. These are the first five digits in the sorted list:
9, 8, 7, 6, 5
Step 4: Calculate the Sum
Add the identified five digits:
Sum = 9 + 8 + 7 + 6 + 5
Sum = 35
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