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The initial image shows 6 tokens arranged in a triangle.

Mathematics

ScanSolve AI Answer

Answer

B\text{B}

Step-by-step solution

5 steps
  1. Analyze the initial configuration of tokens.

    The initial image shows 6 tokens arranged in a triangle.
    Counting the tokens:

    • There are 4 blue tokens (filled circles).
    • There are 2 white tokens (empty circles).
  2. Determine the effect of turning over all tokens.

    The question states that each token has one blue side and one white side. When a token is turned over, its color flips.

    • A blue token will become white.
    • A white token will become blue.
  3. Calculate the final configuration after turning over all tokens.

    Applying the color flip to the initial configuration:

    • The 4 blue tokens will become 4 white tokens.
    • The 2 white tokens will become 2 blue tokens.

    So, the final configuration should have 2 blue tokens and 4 white tokens.

  4. Determine the final arrangement.

    Let's represent the initial arrangement (B for blue, W for white):
    B
    B W
    B B W

    After turning over all tokens, each B becomes W, and each W becomes B:
    W
    W B
    W W B

  5. Compare the final configuration and arrangement with the given options.

    • Option (A) shows 4 blue and 2 white tokens, which is the initial state. Incorrect.
    • Option (B) shows 2 blue and 4 white tokens, arranged as: W W B W W B This matches our calculated final configuration and arrangement. Correct.
    • Option (C) shows 3 blue and 3 white tokens. Incorrect.
    • Option (D) shows 2 blue and 4 white tokens, arranged as: W W B W W B This is identical to option (B) and also matches our calculated final configuration and arrangement. Correct.
    • Option (E) shows 4 blue and 2 white tokens, which is the initial state. Incorrect.

    Since both (B) and (D) are identical and correct, we select one of them.

    The final answer is B\text{B}.

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