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Variable Vault Puzzle

Variable Vault

Variable Vault turns algebraic relationships into a four-dial combination lock you must crack with logic and equations. Each dial (A, B, C, D) is linked by clues – linear equations, sums, or differences – that you solve to reveal the secret code. By translating each verbal hint into a simple formula, you determine the value of each variable and unlock the vault.

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Examples of Variable Vault

Solve Variable Vault Puzzle

Variable Vault turns a set of verbal or numeric clues into a short system of equations – each variable (A, B, C, D) corresponds to a vault digit.

1. List the Clues
  • Write each clue out: “A + B = 7,” “C = 2A,” “B + D = C,” etc.
  • Identify which clues are simple sums/differences and which require substitution or factorisation.

2. Assign Equations
  • For each clue, translate into algebraic form. Number them for reference (1), (2), (3)…

3. Solve Sequentially
  • Start with the simplest equation (often a single variable equals a number).
  • Use that result to substitute into the next clue. Continue until you’ve solved for A, then B, then C, then D.

4. Plug Back & Validate
  • After finding all four values, re-insert them into every clue to ensure consistency.

5. Form the Combination
  • Write down A, B, C, D in order to reveal the vault code (e.g. 5–2–8–3).

Some Pro Tips
  • Keep your equations in tidy columns so you can see how each variable was derived.
  • If one clue yields multiple possibilities (e.g. C² = 16 ⇒ C = ±4), the context (digit range 0–9) will eliminate the negative.
  • Always box your final code and label it clearly as “Vault Combination.”

Example Variable Vault Puzzle

Formulas:
A + B = 3
B + C = 8
A + B + C = 10

Approach:
A + B = 3 therefore 3 + C = 10 therefore C = 7
B + C = 8 therefore B + 7 = 8 therefore B = 1
A + B = 3 therefore A + 1 = 3 therefore A = 2

Answer:
A = 2, B = 1, C = 7
Once you’ve set A, B, C, and D correctly, the vault clicks open – proof you’ve mastered the underlying relationships. Variable Vault trains you to read real-world scenarios as algebraic statements, build and solve short systems of equations, and check your work systematically. With practice, you’ll breeze through any puzzle that asks “What goes where?” and emerge ready for more advanced challenges.

Now lets practice ...

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