Sunday July 31, 2011
Here, you'll be investigating an interesting property of a numerical sequence.
A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before.
For example,
44>>>32>>>13>>>10>>>1>>>1
85>>>89>>>145>>>42>>>20>>>4>>>16>>>37>>>58>>>89
Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most significant is that every starting number will eventually arrive at 1 or 89.
How many starting numbers below one million will arrive at 89?
(This problem and its text come from Project Euler).
For example,
44>>>32>>>13>>>10>>>1>>>1
85>>>89>>>145>>>42>>>20>>>4>>>16>>>37>>>58>>>89
Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most significant is that every starting number will eventually arrive at 1 or 89.
How many starting numbers below one million will arrive at 89?
(This problem and its text come from Project Euler).
Show solution
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