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what is mars the planet - Network4

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 A science educator is designing an experiment for students involving 3 different types of plant seeds: oak, pine, and birch. If students are to plant 6 seeds in a row, how many different arrangements are possible if at least two adjacent seeds must be of the same type?

📌 Next, calculate the number of sequences where no two adjacent seeds are the same. For this, choose a type for the first seed, and each subsequent seed must differ from its predecessor. The first seed has 3 choices. For each subsequent seed, there are 2 choices (it cannot be the same as the immediately previous one).

📌 Now, subtract the sequences with no consecutive seeds of the same type from the total sequences to find those with at least one such pair:

📌 A robotics engineer is programming a robot to assemble items using 4 different types of components: gears, screws, bolts, and springs. The robot assembles a sequence of 8 components. How many sequences are possible if no more than two adjacent components can be identical?

📌 Establish recurrence relations based on the last one or two components:

📌 A sequence ending with two identical components must have come from a sequence ending with one identical component, by repeating its last component:

📌 a_3 = 3a_2 + 3a_1 = 3(16) + 3(4) = 48 + 12 = 60

📌 a_4 = 3a_3 + 3a_2 = 3(60) + 3(16) = 180 + 48 = 228

🔥 Popular Posts

Alternatively, perhaps the arithmetic sequence includes positive and n...
Perhaps the sum is 96? 3(64) + 7(8) = 192 + 56 = 248, no.
But for the purpose of this task, and since the format requires a clea...
Or accept the exact solution is not integer, but thats not typical.
After re-evaluation, perhaps the problem is:
Lets assume its correct and report the precise value as per math.
But Olympiad problems rarely have non-integer answers.
Perhaps I miscalculated S_8: a=5, d=3, n=8
Sequence: 5, 8, 11, 14, 17, 20, 23, 26
Sum: 5+8=13, +11=24, +14=38, +17=55, +20=75, +23=98, +26=124 — correct...

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