If 1 is added to each even digit and 2 is subtracted from each odd digit in the number 39225685459, then how many digits will appear more than twice in the new number thus formed?

Correct Answer: Two

Step 1: Understand the Given Rules
We are given the original number: 39225685459.
We need to form a new number by applying two specific operations:
1. Add 1 to each even digit (0, 2, 4, 6, 8).
2. Subtract 2 from each odd digit (1, 3, 5, 7, 9).

Step 2: Apply the Operations Digit by Digit
Let's transform each digit of the number 39225685459 according to the rules:

• First digit 3 (Odd): $3-2=1$
• Second digit 9 (Odd): $9-2=7$
• Third digit 2 (Even): $2+1=3$
• Fourth digit 2 (Even): $2+1=3$
• Fifth digit 5 (Odd): $5-2=3$
• Sixth digit 6 (Even): $6+1=7$
• Seventh digit 8 (Even): $8+1=9$
• Eighth digit 5 (Odd): $5-2=3$
• Ninth digit 4 (Even): $4+1=5$
• Tenth digit 5 (Odd): $5-2=3$
• Eleventh digit 9 (Odd): $9-2=7$

Step 3: Write down the New Number
Combining the transformed digits in order, the new number formed is:
17333793537

Step 4: Count the Frequencies of Each Digit
Now, let's count how many times each digit appears in 17333793537:
• Digit 1 appears 1 time.
• Digit 3 appears 5 times.
• Digit 5 appears 1 time.
• Digit 7 appears 3 times.
• Digit 9 appears 1 time.

Step 5: Identify Digits Appearing More Than Twice
We are asked to find how many digits appear more than twice (i.e., 3 times or more):
1. The digit 3 appears 5 times (which is > 2).
2. The digit 7 appears 3 times (which is > 2).

Therefore, exactly Two digits ('3' and '7') appear more than twice in the new number.