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Problem 92


Problem 92


Square digit chains

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 → 11
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 amazing is that EVERY starting number will eventually arrive at 1 or 89.

How many starting numbers below ten million will arrive at 89?


平方数字链

将一个数的所有数字的平方相加得到一个新的数,不断重复直到新的数已经出现过为止,这构成了一条数字链。

例如,

44 → 32 → 13 → 10 → 11
85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89

可见,任何一个到达1或89的数字链都会陷入无尽的循环。更令人惊奇的是,从任意数开始,最终都会到达1或89。

有多少个小于一千万的数最终会到达89?