Determine the probability that a for a sevendigit 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.
(In reply to
re(2): computer solution by Charlie)
I decided to code the basic program to reduce the semimanual calculations I had done. Either I had made a small error while using Excel, or, as you had supposed, the number of significant digits may have been the problem. Nonetheless, the program "spit out" the same answer (basically) you had computed:
0.20524025e2
The program only took about a second to run.
dim s(60)
dim p(60)
for a = 0 to 15
for b = 0 to 15
for c = 0 to 15
p = a * b * c
if p > 0 and p < 61 then
p(p) = p(p) + 1
end if
for d = 1 to 15
s = a+b+c+d
s(s) = s(s) + 1
next d
next c
next b
next a
prob = 0
for i = 1 to 60
prob = prob + (s(i)/4096)*(p(i)/61440)
next i
print str$(prob)

Posted by Dej Mar
on 20141225 19:16:17 