Math Puzzle: Finish the Cycle
Briefly

In this number puzzle, a sequence emerges where each number is generated from the sum of the squares of the digits of its predecessor. The puzzle begins with 42 and leads through various transformations of numbers based on this summation rule. After calculating the sums for several predecessors, it becomes evident that the unknown number in the sequence is 20. This intriguing relationship suggests a systematic approach to uncovering hidden values within mathematical sequences.
The sequence of numbers is generated by taking the sum of the squares of the digits of the previous number. Understanding this rule is key to solving the puzzle.
For the unknown number, by applying the rule consistently, we identify that 42 follows from summing the squares of its digits, arriving at the final number of 20.
Read at www.scientificamerican.com
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