Level:
Project ID:
9000148903
Accepted:
1
Clonable:
0
Easy:
0
A combination lock will open if a right choice of three numbers (from
\(1\) to
\(9\)) is selected.
Suppose that we use a brute force attack to open the lock (we try all possibilities). To try one
code takes \(20\)
seconds. What is the maximal time (in seconds) required to open the lock by brute
force?
\(20\cdot 9^{3}\, \mathrm{s}=14\:580\,\mathrm{s}\)
\(20\cdot \frac{9!}
{6!}\, \mathrm{s}=10\:080\,\mathrm{s}\)
\(20\cdot \frac{9!}
{3!\; 6!}\, \mathrm{s}=1\:680\,\mathrm{s}\)
\(20\cdot 9\cdot 3\, \mathrm{s}=540\,\mathrm{s}\)