3^6 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 729

February 22, 2026

$3^6 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 729$

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Therefore, there are \(\boxed{243}\) different planting arrangements possible.
Question:** A science fiction writer imagines a future where memories can be transferred between individuals using a neural interface. If there are 6 distinct memories to be transferred, and each memory can be either stored, shared, or discarded, in how many different ways can the files be processed?
Solution:** Each of the 6 memories has 3 possible outcomes: stored, shared, or discarded. Therefore, for each memory, there are 3 choices. The total number of ways to process all memories is \(3^6\).
Thus, there are \(\boxed{729}\) different ways to process the memories.
Question:** An angel investor is evaluating 4 early-stage biotech startups for potential investment. If the investor decides to pick exactly 2 of these startups to fund, how many different pairs of startups can be chosen?
Solution:** The number of ways to choose 2 startups out of 4 is given by the combination formula \(\binom{n}{k}\), where \(n\) is the total number of startups and \(k\) is the number to choose. Therefore, we calculate \(\binom{4}{2}\).

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