perplexus.info :: Numbers : super powerful pandigitals

super powerful pandigitals (Posted on 2009-02-24)

1) Find all the 0 to 9 pandigital numbers (without leading zero) that have the largest power of 3 as a factor.

2) One of these numbers has a very interesting property. What is it?

*an x to y pandigital number is an integer that contains all the digits from x to y and only those digits once each, for example 1234 is 1 to 4 pandigital but not 1 to 9 pandigital*

See The Solution Submitted by Daniel

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Puzzle Thoughts

Comment 8 of 8 |

The pandigital number with the largest power of 3 as a factor is 7246198035 with the factors 3^15 x 5 x 101.

The eight other pandigital numbers with the factor 3^14 are:

3410256897 = 3^14 x 23 x 31

5361708249 = 3^14 x 19 x 59

5902183746 = 3^14 x 2 x 617

6820513794 = 3^14 x 2 x 23 x 31

8145396207 = 3^14 x 13 x 131

8269753401 = 3^14 x 7 x 13 x 19

9145036728 = 3^14 x 23 x 239

9537240186 = 3^14 x 2 x 997

Posted by K Sengupta on 2024-03-09 20:36:20

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