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Problem 21

Neow’s Counterexample

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Neow’s Counterexample

Earn one jewelRough Diamond OctahedronLevel 2

The problem

In the game Slay the Spire, the Ironclad spends Energy to play cards. He starts this turn with 3 Energy. After each card, subtract its cost. He can keep playing while he can pay the next cost. Ignore other card effects.

Neow claims, “Every hand of three different cards from the table lets the Ironclad play at least two cards.” A counterexample is one allowed hand that makes his word “every” false.

One working turn: start with 3 Energy, play Strike for 1, then play Cleave for 1. The Ironclad has played two cards and has 1 Energy left.

Available cards

Card Energy cost
Strike 1
Cleave 1
Bash 2
Heavy Blade 2
Uppercut 2
Bludgeon 3

Questions

Circle in the table; use separate paper for sums and explanations.

  1. Find a counterexample: circle three different cards in the table. Explain why, no matter which card the Ironclad plays first, he cannot afford a second card.

  2. The picture shows one hand where Neow’s claim works. Why does your one counterexample still prove that his word “every” is false?

How did it feel?

Pick the option that best matches this challenge. Recommendations use topic, math area, grade, story, and thinking challenge.

Keep exploring

Slay the Spire challenge 2 of 4

Full rating evidence

Difficulty & skills

Designed for Grade 3 · Uses Middle Grade 3 math · About 2–7 minutes

Grade 3 · Number and operations · Whole-number operations

MJ 3.3 · C2 · W1

MathJewels rates content readiness, problem-solving challenge, and workload separately. These estimates describe the easiest reasonable solution path and do not reveal the solution.

Content level

MJ 3.3

Grades 3–5

Grade 3 progression · point 3

Likely range
MJ 3.2–3.4
Confidence
84%

Challenge

C2 · Standard

The solver chooses and coordinates familiar methods.

  • Method selection1
  • Reasoning depth2
  • Novelty2
  • Constraint management1
  • Proof or justification2

Workload

W1 · Light

A short response with only a few steps.

Active time
2–7 minutes · typically 4
Response
Short Explanation
Known-method steps
5
  • Mechanical execution1
  • Written output1
  • Representation production1
  • Bookkeeping1

Learning focus

Skills this problem practices

What a successful response demonstrates, with each skill’s share of the content rating.

  • Solve a multi-step word problem

    Organize a contextual problem into an ordered sequence of operations, carry out the steps, and check that the result fits the situation.

    • Developing mastery
    • 65% focus
    • MJ 3.3 milestone

  • Add and subtract whole-number quantities

    Combine and compare whole-number quantities in contextual problems and use addition or subtraction to find an unknown result.

    • Independent mastery
    • 35% focus
    • MJ 2.7 milestone

Readiness

Helpful prerequisites

Skills the rating assumes are already available to the learner.

  • Compose and decompose within 5

    Compose and decompose concrete quantities through 5, including recognizing a whole as two smaller parts in more than one arrangement.

    • Fluent readiness
    • Required
    • MJ 1.0 milestone