Digit Manipulation and Product Calculation

The problem requires modifying a given number based on its digits and then finding the product of repeated digits in the resulting number.

Step 1: Modifying the Number Digits

Start with the original number: 36719542.

• Identify the even digits: 6, 4, 2.
• Add 1 to each even digit:
  • 6 becomes $6 + 1 = 7$
  • 4 becomes $4 + 1 = 5$
  • 2 becomes $2 + 1 = 3$
• The odd digits remain unchanged: 3, 7, 1, 9, 5.
• Form the new sequence of digits by replacing the even digits: 3, (6+1), 7, 1, 9, 5, (4+1), (2+1).
• The new sequence is: 3, 7, 7, 1, 9, 5, 5, 3.
• The new number formed is 37719553.

Step 2: Identifying Repeated Digits

Examine the digits in the new number (37719553) to find those that appear more than once.

• Digit 3 appears 2 times.
• Digit 7 appears 2 times.
• Digit 1 appears 1 time.
• Digit 9 appears 1 time.
• Digit 5 appears 2 times.

The digits repeated more than once are 3, 7, and 5.

Step 3: Calculating the Product of Repeated Digits

Calculate the product of the identified repeated digits (3, 7, and 5).

• Product = $3 \times 7 \times 5$
• Product = $21 \times 5$
• Product = $105$

The product of the digits repeated more than once in the new number is 105.