2010年Puzzleup数学竞赛−第08题: Generating Numbers

castelu

Generating Numbers

Applying the steps below, you will generate a number, on the conditionthat every digit of a number produced in each step is different fromits other digits.

1. Write down a number with one, two or three digits.
2. Delete at most three consecutive digits and in the places of thedeleted digits place the square of the number formed by these digits.
3. For the number you get, repeat steps two and three. If you cannot get a number that satisfies the conditions, stop.

What is the largest number that can be generated through this mechanism?

Example: 307, 3(07), 349, 3(4)9, 3169, ...