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Home » 5: Go Beyond "Olá" – The Sm Party Way to Say Hello in Portuguese Forever! - ClickBalance

5: Go Beyond "Olá" – The Sm Party Way to Say Hello in Portuguese Forever! - ClickBalance

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 Question: Solve for $ x $ in the equation $ 3x + 5 = 2x + 14 $.

📌 Solution: Subtract $ 2x $ from both sides:

📌 Solution: Test divisibility by primes. 221 is not divisible by 2, 3, or 5. Dividing by 13:

📌 Solution: Since the order of addition matters, we are looking for the number of permutations of 5 catalysts taken 2 at a time. This is given by:

📌 Question: A UX researcher is testing 4 interface designs with 6 participants. If each participant tests exactly one design and each design must be tested by at least one participant, how many ways can the participants be assigned to designs?

📌 Solution: This is a classic surjection problem: distributing 6 distinguishable participants to 4 distinguishable designs such that no design is left untested. The number of such surjective functions is given by:

📌 Question: A science policy expert is organizing a roundtable with 3 government officials and 3 industry leaders. If the seating must alternate government and industry around a circular table, how many distinct seating arrangements are possible?

📌 Solution: In a circular arrangement with alternating roles, we fix one persons position to account for rotational symmetry. Fix a government official at one seat. Then the seats alternate: G, I, G, I, G, I. The remaining 2 government officials can be arranged in $2!$ ways, and the 3 industry leaders in $3!$ ways. So the total number of distinct arrangements is:

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