IBM Ponder This #226 · February 2017

When you run the following pseudo code on a sequence of six bits, in exactly 14 cases you get a non-zero value. How many such cases would you get for all sequences of 42 bits?

s=2
r=0
for b in v:
    if (s modulo 7) = b:
        r = r+2*b-1
    s = 6+s*(5+s*s*s*(2+s*(3+s))) + b*(5+s*(5+s*(6+s*s*(3+s*6))))
return r

Bonus question: If we would have asked a similar question for sequences of 14 bits, what would be the connection of the result to IBM?

Hint: We asked a similar bonus question in the past, and the number of solvers was then a multiplication of two prime numbers.

Solution

Best opened after a real attempt

To be added.