BUY BOOKS

Chain Reaction

Chain Reaction unfolds as a sequence of linked problems – each answer becomes the key variable (“a,” “b,” “c,” etc.) in the next equation, so you build and solve a mathematical domino effect. With each step you expand, substitute, and simplify until you reach the final challenge.

Other Puzzle Types

Examples of Chain Reaction

Solve Chain Reaction Puzzle

Chain Reaction puzzles are a multi-stage sequence of linked calculations in which each answer becomes the input for the next problem. Follow these steps every time:

1. Preview the Entire Chain
  • Read all numbered steps first. Note which results feed into later equations (often labeled “a,” “b,” “c,” etc.).
  • Identify any stage that requires expansion, factorisation, or coefficient extraction.

2. Stage-by-Stage Solving
  • Stage 1: Write the first equation exactly. Expand brackets, combine like terms, isolate x, and record “a.”
  • Stage 2: Rewrite the second equation, substituting “a” wherever it appears. Simplify and solve for x to get “b.”
  • Stage 3: If asked to expand an expression like (𝑥+𝑏)(𝑥−1), distribute carefully, then identify the requested piece (e.g. the coefficient of x) and record it as “c.”
  • Subsequent Stages: Continue substituting your most recent result into each new step until you reach the final prompt.

3. Keep Each Result Boxed or Highlighted
  • Visually separate “a,” “b,” “c,” etc., in the boxes or by underlining so you never lose track of which number goes where.

4. Final Verification
  • Once you’ve completed the last step, plug each intermediate value back into its original stage to confirm every equation holds.
  • Expand your final factorisation (if any) to check against the original polynomial.

5. Pro Tips
  • If you spot an early cancellation (e.g. an x² term on both sides), cross it out immediately to simplify subsequent algebra.
  • Use a fresh symbol for each stage—avoid re-using “x” in your workspace for different values.
  • Work slowly on the first few Chain Reactions to build your chain-management skills; the longer chains will feel easy once you’ve internalised the flow.

Example Chain Reaction Puzzle

1. Solve: 2x + 3 = 13
2x = 10
x = 5
a = 5

2. Now solve: a + x = 12
5 + x = 12
x = 7
b = 7

3. Now expand and simplify: (x + b)(x + 1) – what is the constant term?
(x + 7)(x + 1)
x² + 8x + 7
Constant term = 7
c = 7

4. Now solve: (c + x)/2 = 7
(7 + x)/2 = 7
(7 + x) = 7 * 2
x = 14 – 7
x = 7

5. Now factorise: x² + (d)x + 12
x² + 7x + 12
(x + 3)(x + 4)
Completing a Chain Reaction puzzle trains you to keep track of intermediate results, sharpen your substitution skills, and think several moves ahead – just like planning in chess but with algebraic moves.

Now lets practice ...

We have added a selection of our puzzles so that you can practice online: Practice Now