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super powerful pandigitals (Posted on 2009-02-24) |
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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*
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Submitted by Daniel
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Solution:
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As Charlie first pointed out the answer to the first part is 3^15 is the largest power of 3 that can divide a 0 to 9 pandigital number. In researching this problem I simply used a spreadsheet and did not use an exaustive computer program and thus made a slight miscalculation that caused me to belive that 3^14 was the largest power thus leading to the following pandigitals
3410256897
5361708249
5902183746
6820513794
7246198035
8145396207
8269753401
9145036728
9537240186
As for the second part I initially was refering to 5902183746 which when divided by 3^14 leads to 1234 a 1 to 4 pandigital number. Which Charlie also discoverd.
Some other unique properties were discovered by Jer, Ed Bottemiller, and Dej Mar. |
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