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Naught and three poser (Posted on 2010-03-17) Difficulty: 3 of 5
Make a list of the respective minimum values of a positive base N integer, constituted entirely by threes and zeroes, which is divisible by the base ten number 52032 whenever N is a positive integer with 6 ≤ N ≤ 16.

What are the respective smallest number and the largest number in this list?

No Solution Yet Submitted by K Sengupta    
Rating: 1.0000 (1 votes)

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Some Thoughts computer exploration | Comment 1 of 3
list
   20      for N=6 to 16
   30        V=0
   40        for Mult=1 to 10000000
   50         V=V+52032
   60         Num=V
   70         Ns$=""
   80         while Num>0
   90           Ns$=mid("0123456789ABCDEFGH",(Num @ N)+1,1)+Ns$
  100           Num=Num\N
  110         wend
  120         Good=1
  130         for I=1 to len(Ns$)
  140           if instr("30",mid(Ns$,I,1))=0 then Good=0:cancel for:goto 160
  150         next
  160         if Good then:
  170          :print N,Mult;V;Ns$
  175          :cancel for:goto 200
  180         :endif
  190        next
  200      next

run
 6       753057  39183061824 30000033000000
 8       503143  26179536576 303033003300
 10      640625  33333000000 33333000000

that is:
base    multiple       representation
  N     of 52032   base-10       base-N
 
  6      753057  39183061824 30000033000000
  8      503143  26179536576   303033003300
 10      640625  33333000000    33333000000
 

Other bases didn't show results, but there may be for higher multiples of 52032 than the 10,000,000 allowed for here.

 


  Posted by Charlie on 2010-03-17 12:41:54
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