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QwQ: Reflect Deeply on the Boundaries of the Unknown

Nov 27, 2024 - qwenlm.github.io
The article presents a step-by-step solution to the problem of adding a pair of parentheses to the incorrect equation 1 + 2 * 3 + 4 * 5 + 6 * 7 + 8 * 9 = 479 to make it true. The author uses the order of operations (PEMDAS) to calculate the current value of the left side of the equation without any parentheses, which equals 141, not 479. The author then explores various possibilities for where to place the parentheses to alter the order of operations and achieve the desired result.

After testing many different combinations, the author finds that by adding parentheses around (3 + 4 * 5 + 6), and multiplying that sum by 2 and 7, the equation becomes true. The corrected equation is: 1 + 2 * (3 + 4 * 5 + 6) * 7 + 8 * 9 = 479. The author emphasizes the importance of understanding the order of operations and considering different possibilities when solving such problems.

Key takeaways:

  • The initial equation 1 + 2 * 3 + 4 * 5 + 6 * 7 + 8 * 9 = 479 is incorrect and needs a pair of parentheses added to make it true.
  • The order of operations, PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), is used to solve the equation.
  • Several different possibilities for where to place the parentheses were explored, with the correct placement being around (3 + 4 * 5 + 6).
  • The corrected equation is 1 + 2 * (3 + 4 * 5 + 6) * 7 + 8 * 9 = 479.
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