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25 Sep 2025, 06:31
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2 iterations: 5,836
4 iterations: 5,324
Umbrella Corporation monitors a network of 6,000 computers. At the start of the virus outbreak, 4 of these computers get infected. The infection weakens with each round of spreading:
• In the first iteration, each of the 4 initially infected machines infects 8 others.
• In the second iteration, each machine infected in the first iteration infects 4 others.
• In the third iteration, each machine infected in the second iteration infects 2 others.
• In the fourth iteration, each machine infected in the third iteration infects 1 other.
Select for 2 iterations the number of computers that remain uninfected after two iterations are completed, and select for 4 iterations the number of computers that remain uninfected after four iterations are completed. Make only two selections, one in each column.
• In the first iteration, each of the 4 initially infected machines infects 8 others.
• In the second iteration, each machine infected in the first iteration infects 4 others.
• In the third iteration, each machine infected in the second iteration infects 2 others.
• In the fourth iteration, each machine infected in the third iteration infects 1 other.
Select for 2 iterations the number of computers that remain uninfected after two iterations are completed, and select for 4 iterations the number of computers that remain uninfected after four iterations are completed. Make only two selections, one in each column.
| 2 iterations | 4 iterations | |
| 5,260 | ||
| 5,324 | ||
| 5,452 | ||
| 5,488 | ||
| 5,836 | ||
| 5,872 |
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Official Answer
2 iterations: 5,836
4 iterations: 5,324
25 Sep 2025, 06:31
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Official Solution:
The network contains 6,000 computers in total, and the outbreak begins with 4 of them infected.
Iteration 1: Each of the 4 infects 8 others, producing 32 new infections. Adding these to the initial 4 gives 36 infected computers.
Iteration 2: The 32 from the first round each infect 4 others, producing 128 new infections. Adding this to the 36 infected so far gives a cumulative total of 164 after two iterations. The number of unaffected computers is 6,000 − 164 = 5,836.
Iteration 3: The 128 from the second round each infect 2 others, producing 256 new infections. Cumulative total = 164 + 256 = 420.
Iteration 4: The 256 from the third round each infect 1 other, producing 256 new infections. Cumulative total = 420 + 256 = 676 after four iterations. The number of unaffected computers is 6,000 − 676 = 5,324.
Correct answer:
2 iterations "5,836"
4 iterations "5,324"
Bunuel
The network contains 6,000 computers in total, and the outbreak begins with 4 of them infected.
Iteration 1: Each of the 4 infects 8 others, producing 32 new infections. Adding these to the initial 4 gives 36 infected computers.
Iteration 2: The 32 from the first round each infect 4 others, producing 128 new infections. Adding this to the 36 infected so far gives a cumulative total of 164 after two iterations. The number of unaffected computers is 6,000 − 164 = 5,836.
Iteration 3: The 128 from the second round each infect 2 others, producing 256 new infections. Cumulative total = 164 + 256 = 420.
Iteration 4: The 256 from the third round each infect 1 other, producing 256 new infections. Cumulative total = 420 + 256 = 676 after four iterations. The number of unaffected computers is 6,000 − 676 = 5,324.
Correct answer:
2 iterations "5,836"
4 iterations "5,324"
