Puzzle #102: The Persistence Puzzle

This is yet another famous puzzle from the Martin Gardner collection. I was made aware of this one by my nephew, Karan Sharma – thank you! I have not looked up the answer to this one, so do not know how easy or difficult the solution is, but I look forward to doing it myself and also seeing the answers from many of you.

A number’s persistence is the number of steps required to reduce it to a single digit by multiplying all its digits to obtain a second number, then multiplying all the digits of that number to obtain a third number, and so on until a one-digit number is obtained. For example, 77 has a persistence of four because it requires four steps to reduce it to one digit: 77-49-36-18-8. The smallest number of persistence one is 10, the smallest of persistence two is 25, the smallest of persistence three is 39, and the smaller of persistence four is 77. What is the smallest number of persistence five?

As always, please send your answers directly to me at alokgoyal_2001@yahoo.com. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.

 

Be persistent with this puzzle šŸ™‚

 

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