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Home » \( 1 - 5 + 6 - 4 = -2 - Rice University

\( 1 - 5 + 6 - 4 = -2 - Rice University

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 Question: An archaeologist discovers 7 distinct pottery shards from a Peruvian site and 5 from a Mesoamerican site. If she arranges them in a row on a shelf with all Peruvian shards indistinct and all Mesoamerican shards indistinct, how many distinct arrangements are possible?

📌 Solution: The problem reduces to permutations of a multiset. There are $ 7 + 5 = 12 $ total shards, with 7 identical Peruvian and 5 identical Mesoamerican. The number of distinct arrangements is $

📌 Question: A hydrologist models groundwater flow through 3 layers of soil, each with 2 possible flow channels (A or B). If the system must have exactly 2 channels flowing vertically and 1 horizontally, how many distinct flow configurations are possible?

📌 Question: An entomologist tracks 5 types of pollinators visiting 3 flower species. If each pollinator visits exactly one flower per day for 2 days, how many distinct 2-day visitation sequences are possible?

📌 Question: An archaeologist excavates 4 stone tablets and 3 ceramic vessels. If she displays them in a row with the tablets indistinct among themselves and the vessels indistinct among themselves, how many distinct arrangements are possible?

📌 Solution: The problem is equivalent to arranging 4 identical tablets and 3 identical vessels. The number of distinct arrangements is $

📌 Question: A hydrologist simulates water movement through 6 underground aquifers, each with 2 possible directions (left or right). If the system must have exactly 4 leftward flows and 2 rightward flows, how many distinct flow patterns are possible?

📌 A lunar regolith extraction engineer needs to determine how many two-digit integers can evenly distribute the weight of a mining vehicle that needs to hold on average 13.5 kilograms. These integers must be divisible by 3. How many such integers exist?

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