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 Hexadecimal Digit Travail (Posted on 2014-12-25)
Determine the probability that a for a seven-digit positive hexadecimal integer N, the sum of the first four digits of N is equal to the product of the last three digits of N.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution | Comment 1 of 5
516504/251658240 = 21521/10485760 ~= 0.002052402

from

pr\$ = Chr\$(1)
For v = fromBase("1000000", 16) To fromBase("fffffff", 16)
overct = overct + 1
h\$ = base\$(v, 16)
tot = 0: prod = 1
For i = 1 To 4
tot = tot + fromBase(Mid(h\$, i, 1), 16)
Next
For i = 5 To 7
prod = prod * fromBase(Mid(h\$, i, 1), 16)
Next
If tot = prod Then
ct = ct + 1
'     Text1.Text = Text1.Text & h\$ & crlf
'     DoEvents
End If
If Left(h\$, 1) <> pr\$ Then Text1.Text = Text1.Text & h\$ & crlf: DoEvents
pr\$ = Left(h\$, 1)
Next v
g = gcd(ct, overct)

Text1.Text = Text1.Text & crlf & ct & Str(overct) & Str(ct / g) & Str(overct / g) & mform(ct / overct, "##0.000000000") & crlf: DoEvents

The output included the hex value every time the first digit changed, as the whole process took over 1/2 hour run time, I needed a progress indication:

1000000
2000000
3000000
4000000
5000000
6000000
7000000
8000000
9000000
a000000
b000000
c000000
d000000
e000000
f000000

516504 251658240 21521 10485760  0.002052402
done

 Posted by Charlie on 2014-12-25 14:01:32

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