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The initial image shows 6 tokens arranged in a triangle.
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Step-by-step solution
5 stepsAnalyze 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).
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.
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.
Determine the final arrangement.
Let's represent the initial arrangement (B for blue, W for white):
B
B W
B B WAfter turning over all tokens, each B becomes W, and each W becomes B:
W
W B
W W BCompare 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 .
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