Problem 13 · Lakitu’s Hidden Boost SettingPrint one blank worksheet now, or prepare a family or classroom packet.
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Lakitu’s Hidden Boost Setting

Earn one jewelMaster-Cut ZirconLevel 5

On a straight Mario Kart practice track, the checkpoints are numbered 0, 1, 2, 3, and so on. Mario starts at checkpoint 0. Every mini-turbo moves him forward exactly 4 checkpoints.

Every Mushroom moves the same hidden whole-number distance. That distance is more than 4 but less than 11 checkpoints. Mario may reuse either move in any order and may stop after any move.

Lakitu says, “Checkpoint 17 is the greatest-numbered checkpoint Mario cannot land on exactly.”

Mario lines up another run on Lakitu’s practice track.

Known move shown · Mushroom landing stays hidden

Mario Kart practice-track number line A number line marks whole-number checkpoints 0 through 10 and continues right. A blue arc shows that one mini-turbo moves from 0 to 4. A red label says the Mushroom move is one hidden whole number from 5 through 10; its landing point is not shown. +4 MINI-TURBO MUSHROOM + ? · 5–10 START CHECKPOINTS CONTINUE →
SettingCan 17 be reached?Evidence
5
6
7
8
9
10

Mushroom setting: ______

Your challenge

  1. How many checkpoints does one Mushroom move Mario? Prove that no other allowed setting can make Lakitu’s statement true.
  2. For your setting, prove that Mario cannot land on checkpoint 17 and that he can land on every checkpoint greater than 17.

Record settings 5–10 here. Use separate paper for your proof with number-line jumps or multiplication equations. Checking only a few checkpoints is not a proof.

Keep exploring

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Full rating evidence

Difficulty & skills

Designed for Grade 3 · Uses Middle Grade 3 math · About 13–30 minutes

Grade 3 · Number and operations · Number lines · Equal groups · Whole-number operations

MJ 3.3 · C5 · W3

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 3.1–3.5
Confidence
86%

Challenge

C5 · Olympiad

A sustained original strategy with several significant insights and proof.

  • Method selection3
  • Reasoning depth3
  • Novelty3
  • Constraint management3
  • Proof or justification3

Workload

W3 · Heavy

Sustained mathematical work and a substantial written response.

Active time
13–30 minutes · typically 20
Response
Proof
Known-method steps
16
  • Mechanical execution2
  • Written output3
  • Representation production3
  • Bookkeeping3

Learning focus

Skills this problem practices

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

  • Use number-line structure

    Use order and equal distances on a number line to determine and justify relationships among whole-number positions.

    • Transfer mastery
    • 30% focus
    • MJ 3.3 milestone
  • Reason about odd and even numbers

    Determine whether a whole number can be paired or split into two equal whole-number groups and use that structure in an explanation.

    • Transfer mastery
    • 25% focus
    • MJ 3.3 milestone
  • Multiply equal groups

    Represent and solve whole-number situations made from equal groups, including choosing and evaluating a multiplication equation.

    • Independent mastery
    • 25% focus
    • MJ 3.2 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.

    • Fluent mastery
    • 20% focus
    • MJ 3.2 milestone

Readiness

Helpful prerequisites

Skills the rating assumes are already available to the learner.

  • Use number-line structure

    Use order and equal distances on a number line to determine and justify relationships among whole-number positions.

    • Fluent readiness
    • Required
    • MJ 2.8 milestone
  • Reason about odd and even numbers

    Determine whether a whole number can be paired or split into two equal whole-number groups and use that structure in an explanation.

    • Fluent readiness
    • Required
    • MJ 2.8 milestone
  • Multiply equal groups

    Represent and solve whole-number situations made from equal groups, including choosing and evaluating a multiplication equation.

    • Independent readiness
    • Required
    • MJ 3.2 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.

    • Fluent readiness
    • Required
    • MJ 3.2 milestone