2026 AMC 8 Problem 1: Solution

Work through 2026 AMC 8 Problem 1 on arithmetic expressions with a written solution, hints, and a visual explanation.

AlgebraLevel 1 · Warmup

What is the value of the following expression? 1 + 2 − 3 + 4 + 5 − 6 + 7 + 8 − 9 + 10 + 11 − 12

  • A. 18
  • B. 21
  • C. 24
  • D. 27
  • E. 30
Hints
  1. Look at the pattern of signs — every third term is subtracted. Try grouping the terms in sets of three.
  2. Each group of three (like 1 + 2 − 3) simplifies to a single small number — find that number for each group.
  3. Add up the four group totals to get the final value.
Read the step-by-step solution

Answer: A · 18

  1. Group terms in threes

    Group the expression into sets of three consecutive terms: (1 + 2 − 3) + (4 + 5 − 6) + (7 + 8 − 9) + (10 + 11 − 12).

  2. Evaluate each group

    Each group simplifies to: 0 + 3 + 6 + 9 = 18.

    0 + 3 + 6 + 9 = 18

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