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super powerful pandigitals (Posted on 2009-02-24) Difficulty: 3 of 5
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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Solution 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   end
OK
displays:

run
1023456789       4
1023458976       4
1023459786       4
1023459867       6
1023487569       7
1023489756       8
1025897643       9
1027865943       10
1029578364       11
1250834967       11
1257389406       12
1359426078       12
1742063598       12
2081654397       12
2095471863       12
2170936485       12
2304859617       12
2415930786       12
2419650873       12
2548791036       12
2934085761       12
3410256897       14
5361708249       14
5902183746       14
6820513794       14
7246198035       15
OK

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       14
5361708249       14
5902183746       14
6820513794       14
7246198035       15
8145396207       14
8269753401       14
9145036728       14
9537240186       14

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