The sum of three consecutive integers is equal to their product. How many such possibilities are there?

Correct Option (3)

There are precisely three sets of consecutive integers for which their sum equals their product. These sets are:

• The set (-1, 0, 1):
  • Sum: (-1) + 0 + 1 = 0
  • Product: (-1) × 0 × 1 = 0
  • Here, the sum is equal to the product.
• The set (1, 2, 3):
  • Sum: 1 + 2 + 3 = 6
  • Product: 1 × 2 × 3 = 6
  • Here, the sum is equal to the product.
• The set (-3, -2, -1):
  • Sum: (-3) + (-2) + (-1) = -6
  • Product: (-3) × (-2) × (-1) = -6
  • Here, the sum is equal to the product.

Since three distinct sets satisfy the given condition, there are three such possibilities.

Incorrect Options:

Options (1), (2), and (4) are incorrect because the analysis demonstrates the existence of exactly three sets of consecutive integers whose sum is equal to their product. Therefore, stating "Only one", "Only two", or "No such possibility is there" is factually inaccurate based on the derived solutions.