Math Puzzle: Discover the Secret System

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The numbers on this triangle are organized in line with a sure system. What would the following row be?

In every row n of the triangle, the integers from 1 to n are in alphabetical order. Within the subsequent row the quantity 8 can be added, and since “eight” comes earlier than “five” in alphabetical order, it should be firstly of the row, giving us this sequence:

8 5 4 1 7 6 3 2

(Be aware that Scientific American’s editors needed to modify the order on this one from the unique German.)

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This puzzle initially appeared in Spektrum der Wissenschaft and was reproduced with permission.

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