So total: 4 distinct arrangements (one per suit)
**So
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- But if numbers are indistinguishable in value (e.g., heart 10 same as diamond 10 if indistinct), but rank matters, then only fixed sequence counts.
- For each suit, only one valid royal flush sequence (A-K ordered)
- No permutations—order is fixed (A-K)
- But arrange implies ordering — if the hand is ordered (like in poker), but royal flush sequences are fixed. However, in permutations, even if order is fixed by rank, the arrangement of 5 specific cards in a sequence is just one per suit.
- But the phrase clickbait suggests surprising difficulty—perhaps permuting the suits? No—only one valid.
- Wait — perhaps the indistinguishable applies to the value representation: if all 10s are identical in value, but still A-10 requires distinct ranks.
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Set \( u + rac{1}{u} = 2 \). Multiply by \(u\): \( u^2 - 2u + 1 = 0 \Rightarrow (u - 1)^2 = 0 \Rightarrow u = 1 \), still.
So \( rac{z + w}{z - w} = 1 \Rightarrow z + w = z - w \Rightarrow
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