Exercise 2: Estimating a 6-Digit PIN Search at the Measured Rate — Possible Solution
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THE ESTIMATE
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This chapter measured a real rate of approximately 2.58 million checks
per second for the 3-digit PIN search. A 6-digit PIN has exactly
1,000,000 possible values.

    estimated time = 1,000,000 / 2,582,888 checks-per-second
                    = approximately 0.387 seconds

So an exhaustive search of every possible 6-digit PIN would take well
under half a second at the same measured rate.

WHY THIS IS STILL A REASONABLE BRUTE-FORCE CANDIDATE
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Even though the 6-digit search space is exactly 1,000 times larger
than the 3-digit search space (1,000,000 versus 1,000), the actual
time required only grew by that same factor of 1,000 - from about
0.187 milliseconds to about 387 milliseconds. This is because the
search space here grows LINEARLY as more digits are added (each
additional digit multiplies the space by exactly 10), not
exponentially the way the subset-sum problem's 2^n space does. A
linear relationship between problem size and search space means the
time needed scales in direct, predictable proportion - going from
"instant" to "still under half a second" is a completely tolerable
cost for three extra digits of security, unlike the subset-sum
example where each additional item DOUBLES the entire remaining
search space.

WHY THIS WORKS AS AN ANSWER
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The estimate is computed directly from this chapter's own measured
rate rather than a fresh assumption, and the explanation correctly
identifies why the resulting time (well under a second) is still
reasonable - by contrasting the linear growth of a fixed-digit-count
PIN space against the exponential growth this chapter's own subset
example demonstrated, rather than simply asserting "it's still fast."