A Puzzle A Day: 2026-04-29

An alien civilization sends out a fleet of 7 identical explorer ships to scan for habitable planets. Each ship is assigned to scan a different sector of the galaxy. After completing its scan, each ship reports the number of habitable planets it found. The first ship reports finding 3 habitable planets, the second reports 4, the third reports 5, and so on, with each subsequent ship reporting one more habitable planet than the previous one. However, due to overlapping sectors, it is later discovered that for every ship (from the second ship onwards), exactly one of the planets it found was *already found by the very first ship*. All other planets found by any ship were unique to that ship's specific discoveries (apart from the single overlap with the first ship). How many *unique* habitable planets were found in total across all 7 ships?
Correct: 36
Let's break down the unique planet discoveries: 1. The first ship reports 3 habitable planets. These are all unique to begin with. 2. The second ship reports 4 planets. But exactly one of these was already found by the first ship. So, the second ship adds 4 - 1 = 3 *new* unique planets to the total count. 3. The third ship reports 5 planets. Similarly, one of these was already found by the first ship. So, it adds 5 - 1 = 4 *new* unique planets. 4. The fourth ship reports 6 planets, adding 6 - 1 = 5 *new* unique planets. 5. The fifth ship reports 7 planets, adding 7 - 1 = 6 *new* unique planets. 6. The sixth ship reports 8 planets, adding 8 - 1 = 7 *new* unique planets. 7. The seventh ship reports 9 planets, adding 9 - 1 = 8 *new* unique planets. To find the total number of unique planets, we sum the unique discoveries from the first ship and all the *new* unique discoveries from the subsequent ships: Total unique planets = (Planets from Ship 1) + (New from Ship 2) + (New from Ship 3) + (New from Ship 4) + (New from Ship 5) + (New from Ship 6) + (New from Ship 7) Total unique planets = 3 + 3 + 4 + 5 + 6 + 7 + 8 = 36. A common mistake would be to simply sum all the reported planets (3+4+5+6+7+8+9 = 42), which doesn't correctly account for the single planet shared with the first ship across the other six missions.
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