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 Casting Out Zeros (Posted on 2013-07-25)
One may perform the following two operations on a natural number:

1.Multiply it by any natural number
2.Delete zeros in its decimal representation.

For any natural number n, can one perform a sequence of these operations that will transform n to a one-digit number?

 No Solution Yet Submitted by Danish Ahmed Khan No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Godel strikes again --- 31 and 33 | Comment 2 of 4 |
(In reply to Godel strikes again by Steve Herman)

`? 31`
`mult     prod   w/o zeros 97      3007    37 11      407     47 64      3008    38 55      2090    29 69      2001    21 48      1008    18 5       90      9`
`? 33 31      1023    123 82      10086   186 54      10044   144 75      10800   18 5       90      9`

from

10     N0=1
20     while N0>0
30       input N0
40       if N0=0 then end
50       N=N0:Pn=0
60       while N>9 and N<>Pn
65          Pn=N
70         Max0=-1:Besti=1:Bestprod=N
80         for I=1 to 99
90            Prod=N*I
100            Z=fnCtzero(Prod)
110            if Z>Max0 and I @ 10<>0 and fnNozero(Prod)<>N then Max0=Z:Besti=I:Bestprod=Prod
120         next I
130         N=fnNozero(Bestprod)
140         print Besti,Bestprod,N
150       wend
160     wend
170
180     fnCtzero(Num)
190        local Ct,I,Ns
200        Ns=str(Num)
210        Ct=0
220        for I=1 to len(Ns)
230          if mid(Ns,I,1)="0" then inc Ct
240        next
250     return(Ct)
260
270     fnNozero(Num)
280        local Ns,N,I
290        Ns=cutspc(str(Num))
300        N=0
310        for I=1 to len(Ns)
320          if mid(Ns,I,1)>"0" then N=10*N+val(mid(Ns,I,1))
330        next
340     return(N)

 Posted by Charlie on 2013-07-26 09:53:15
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