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 Naught and three poser (Posted on 2010-03-17)
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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 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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