Daily Math Puzzle: 2026-10-16
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2026-10-16
A cutting-edge starship relies on 'prime-core' fuel cells, each identified by a unique positive integer. To prevent catastrophic energy feedback, the ship's AI safety protocol dictates that two fuel cells can only be activated simultaneously if they share *exactly one distinct prime factor*. If they share zero, or more than one, the system locks. A critical hyperspace jump requires activating a compatible pair from the available fuel cells: 28, 42, 55, 63. Which pair can the chief engineer safely activate?
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Solution
Cell 28 and Cell 63 — To solve this, we first find the distinct prime factors for each fuel cell:
* Cell 28: 2² × 7. Distinct prime factors: {2, 7}
* Cell 42: 2 × 3 × 7. Distinct prime factors: {2, 3, 7}
* Cell 55: 5 × 11. Distinct prime factors: {5, 11}
* Cell 63: 3² × 7. Distinct prime factors: {3, 7}
Now we evaluate each pair based on the rule: 'exactly one distinct common prime factor':
* **A. Cell 28 and Cell 42:** Common distinct prime factors are {2, 7}. Count = 2. (Incorrect)
* **B. Cell 42 and Cell 55:** Common distinct prime factors are {}. Count = 0. (Incorrect)
* **C. Cell 28 and Cell 63:** Common distinct prime factors are {7}. Count = 1. (Correct! This pair can be safely activated.)
* **D. Cell 55 and Cell 63:** Common distinct prime factors are {}. Count = 0. (Incorrect)
Therefore, only Cell 28 and Cell 63 share exactly one distinct prime factor (which is 7).
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