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 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 No Rating

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 Hmmmm.... (computer solution? -- spoiler) | Comment 1 of 7
`list - 900   10    N="1023456789"   20    while left(N,1)>"0"   30        V=val(N)   35        Pwr=0   40        while V@3=0   50           V=V//3:inc Pwr   60        wend   70        if Pwr>=Maxp then Maxp=Pwr:print N,Pwr   80        gosub *Permute(&N)   90    wend  900   endOK`
`displays:`
`run1023456789       41023458976       41023459786       41023459867       61023487569       71023489756       81025897643       91027865943       101029578364       111250834967       111257389406       121359426078       121742063598       122081654397       122095471863       122170936485       122304859617       122415930786       122419650873       122548791036       122934085761       123410256897       145361708249       145902183746       146820513794       147246198035       15OK`

These show the largest powers of 3 found up to that point (so once a 14th power is found, 12th powers are no longer shown).

The final power of 3 is 15, but only one pandigital has this power of 3 as a factor.

Those pandigitals with a factor of 3 to the 14th or 15th power are:

`3410256897       145361708249       145902183746       146820513794       147246198035       158145396207       148269753401       149145036728       149537240186       14`

 Posted by Charlie on 2009-02-24 12:36:51

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