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Equation Detective Puzzle

Equation Detective – Level 1 – Hard

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Four friends – Lily, James, Aiden, and Sophia – each bought a different item: wrap, smoothie, panini, or soup. Each made their purchase on a different weekday: Monday, Tuesday, Wednesday, or Friday.


Each item had a different price.

Read more about how to solve these puzzles here

Clues:

  1. The wrap cost £3 less than the smoothie.
  2. Sophia didn’t buy anything on Wednesday, Monday, or Tuesday.
  3. Lily spent £4 more than the person who bought the soup.
  4. Aiden did not buy the panini.
  5. The total cost of Lily and James’s items was £17.
  6. The smoothie cost £9 on Wednesday.
  7. The soup was not purchased on Friday, but did cost £5.
  8. James did not buy the smoothie or the soup.
  9. The person who bought the wrap spent £6.
  10. Aiden made his purchase on Tuesday for £5.

Your Workings For Equation Detective

Enter your working out in this box, including your suggested solution.
Your Answers:
Name Food Day Price
Lily
James
Aiden
Sophie

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Additional instructions for Equation Detective (Level 1, Hard)

Equation Detective – Hard

Hard puzzles rely heavily on indirect deductions. Expect to use elimination repeatedly and to combine three or more clues into a single conclusion.

How to approach:

  • Start with all definitive placements, but expect there to be fewer.
  • Write every relationship clue as algebra/constraints (e.g. A = B + 2, C = 2B, X ≠ Friday).
  • After each new placement, pause and ask: what new eliminations are forced in every category?

Hard-mode tip: re-reading clues is not repetition — the meaning changes as the grid fills. That’s where the hidden deductions appear.

Full help: Equation Detective

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