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 Pieces of eight (Posted on 2015-07-15)
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 No Rating

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 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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