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Pieces of eight (Posted on 2015-07-15) Difficulty: 2 of 5
Consider a product P=8*(888...888), i.e. 8 times a number represented by a chain of k eights.

For what value of k the sum of P's digits is exactly 1000?

No Solution Yet Submitted by Ady TZIDON    
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Solution some computer aid Comment 2 of 2 |
 k   P    s.o.d.
 1   64   10 
 2   704   11 
 3   7104   12 
 4   71104   13 
 5   711104   14 
 6   7111104   15 
 7   71111104   16 
 8   711111104   17 
 9   7111111104   18 
 10   71111111104   19 
 11   711111111104   20 
 12   7111111111104   21 
 13   71111111111104   22 
 14   711111111111104   23 
 15   7111111111111104   24 
 16   71111111111111104   25 
 17   711111111111111104   26 
 18   7111111111111111104   27 
 19   71111111111111111104   28 
 20   711111111111111111104   29 
 
The sum of digits is 9 higher than k.

For sod=1000, use k=991.

    3   kill "pieceof8.txt"
    4   open "pieceof8.txt" for output as #2
    5   Rhf=8:P=8*Rhf:print 1,P,10:print #2,1,P,10
   10   for K=2 to 20
   20     Rhf=10*Rhf+8
   30     Sod=0
   40     S=cutspc(str(8*Rhf))
   50     for I=1 to len(S)
   60        Sod=Sod+val(mid(S,I,1))
   70     next
   80     print K,8*Rhf,Sod
   81     print #2,K,8*Rhf,Sod
  100   next K
  110   close #2


  Posted by Charlie on 2015-07-15 10:46:46
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