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Home » From Fluffy To Fierce: The Untold Stories Behind Every SPIDERMAN Character! - inBeat

From Fluffy To Fierce: The Untold Stories Behind Every SPIDERMAN Character! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: An elementary school student has 5 identical red blocks, 4 identical blue blocks, and 3 identical green blocks. How many distinct towers can she build stacking all 12 blocks in a line?

📌 Solution: The student is arranging a total of $5 + 4 + 3 = 12$ blocks, with indistinguishability within each color. The number of distinct towers is the multinomial coefficient:

📌 Question: An ichthyologist tags 7 fish in a reef: 2 clownfish, 3 parrotfish, and 2 angelfish. If she observes one tagged fish each day for a week, how many distinct sequences of observed species can occur, assuming fish of the same species are indistinguishable?

📌 Solution: The ichthyologist observes 7 fish over 7 days—2 clownfish (C), 3 parrotfish (P), and 2 angelfish (A). Since fish of the same species are indistinguishable, the number of distinct observation sequences is:

📌 Question: A circular park has 5 distinguishable trees planted around its perimeter and 3 indistinguishable benches to be placed among them. If rotations of the arrangement are considered identical, how many distinct arrangements are possible?

📌 Solution: First, fix one tree to account for rotational symmetry. Since the trees are distinguishable, fixing one eliminates rotational duplicates. The remaining 4 distinguishable trees can be arranged in $4! = 24$ ways around the circle.

📌 Now, we place 3 indistinguishable benches into the 5 gaps between the trees (since the trees form a circle, there are 5 gaps between adjacent trees). The number of ways to distribute 3 indistinguishable benches into 5 distinguishable gaps (with no restriction on how many per gap) is a stars and bars problem:

📌 Since the tree arrangements are fixed in relative order by rotation, and benches are placed in gaps (not among trees), and trees are already arranged with one fixed, the total number of distinct arrangements is:

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