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Problem 11 · The Oran Berry Passing CircleOnly the worksheet will be included when you print.
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Name
Date

Pokémon berry mystery

The Oran Berry Passing Circle

Jewel value 36 jewels

Pikachu, Eevee, and Bulbasaur each start with a positive whole number of Oran Berries. They make these three passes in order, and every pass works: Pikachu gives Eevee exactly as many berries as Eevee has then; Eevee gives Bulbasaur exactly as many berries as Bulbasaur has then; Bulbasaur gives Pikachu exactly as many berries as Pikachu has then. After the third pass, all three Pokémon have the same number of berries.

1
Pikachu → EeveeMatch Eevee's pile
2
Eevee → BulbasaurMatch Bulbasaur's pile
3
Bulbasaur → PikachuMatch Pikachu's pile

Questions

Use separate paper for all work and answers.

  1. What is the smallest possible total number of berries they could have at the start?

  2. For that smallest total, how many berries did Pikachu, Eevee, and Bulbasaur each start with? Show all three passes to check your answer.

  3. Prove that no smaller starting total can work.

Teacher & family guide

Difficulty & skills

Grade 2 · Number and operations · Whole-number operations · Equal groups

MJ 2.7 · 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 2.7

Grades K–2

Grade 2 progression · point 7

Likely range
MJ 2.5–3.0
Confidence
88%

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
12–28 minutes · typically 18
Response
Proof
Known-method steps
12
  • 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.

  • Double and halve whole-number quantities

    Use the inverse relationship between doubling a whole-number quantity and splitting an even quantity into two equal whole-number parts.

    • Independent mastery
    • 45% focus
    • MJ 2.6 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.

    • Independent mastery
    • 25% focus
    • MJ 2.5 milestone

  • Add and subtract quantities

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

    • Independent mastery
    • 30% focus
    • MJ 2.7 milestone

Readiness

Helpful prerequisites

Skills the rating assumes are already available to the learner.

  • Double and halve whole-number quantities

    Use the inverse relationship between doubling a whole-number quantity and splitting an even quantity into two equal whole-number parts.

    • Developing readiness
    • Required
    • MJ 2.3 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.

    • Independent readiness
    • Required
    • MJ 2.5 milestone

  • Add and subtract quantities

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

    • Independent readiness
    • Required
    • MJ 2.7 milestone

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