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Systems Administrator calculations with worked answers

Updated 15 September 2026 · 2 min read

Systems administration involves small calculations with large consequences. Choose the wrong RAID level and a server holds less than promised, or loses data when a disk fails. Misread a permission mode and a confidential folder becomes readable by everyone. The examples below show the working for each kind, and every figure was checked by independent code before publication.

How this guide was made

Written for this site with AI assistance, then checked automatically before publishing. The topic table, sample questions, worked examples and study plan are generated from this site’s question bank: each worked example is recalculated by separate code, and each sample answer says where it came from.

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Worked examples

Try each one on paper first. Every figure is generated and then recalculated by separate code before it is published.

  1. Usable space in RAID 1

    A server has 2 × 4 TB disks in RAID 1. How much usable capacity is there, and what failure can it survive?

    Show the working
    1. RAID 1 mirrors two disks, so you get the capacity of one.
    2. Usable = 4 TB
    3. It survives one disk failure.

    Answer: 4 TB; survives one disk failure

  2. Subnet details for a /25 address

    A host is configured as 172.18.54.180/25. Find the subnet mask, network address, broadcast address, usable host range and number of usable hosts.

    Show the working
    1. /25 means 25 network bits, so the mask is 255.255.255.128.
    2. The interesting octet is the fourth, where the mask is 128. Block size = 256 − 128 = 128.
    3. The network address is the multiple of 128 at or below the address in that octet: 172.18.54.128.
    4. The broadcast is one below the next network: 172.18.54.255.
    5. Usable hosts run from 172.18.54.129 to 172.18.54.254: 2^7 − 2 = 126 addresses.

    Answer: Mask 255.255.255.128, network 172.18.54.128, broadcast 172.18.54.255, hosts 172.18.54.129–172.18.54.254 (126 usable)

  3. Reading permissions as an octal mode

    ls -l shows a file as -rwx-----x. What octal mode would you pass to chmod to set exactly these permissions?

    Show the working
    1. Ignore the first character (file type). Split the rest into owner, group and others, three characters each.
    2. Score each triple: r = 4, w = 2, x = 1, dash = 0.
    3. owner rwx = 4 + 2 + 1 = 7; group --- = 0 = 0; others --x = 1 = 1
    4. Mode = 701, so the command is chmod 701 file.

    Answer: 701

  4. Keyspace and entropy of a password policy

    A password of 6 characters is chosen at random from digits only (10 possible symbols). How many bits of entropy does it have, and how long would trying every combination take at 10 billion guesses a second?

    Show the working
    1. Entropy = length × log₂(symbols) = 6 × log₂(10) = 6 × 3.322
    2. = 19.9 bits
    3. Combinations = 10^6 ≈ 1.00e+6
    4. Time to try them all = combinations ÷ 10¹⁰ ≈ 0 seconds. On average an attacker finds it in half that.
    5. This only holds for truly random passwords. A human-chosen word with a digit on the end falls to a dictionary attack far sooner.

    Answer: 19.9 bits; about 0 seconds to exhaust

  5. Usable space in RAID 6

    A server has 5 × 2 TB disks in RAID 6. How much usable capacity is there, and what failure can it survive?

    Show the working
    1. RAID 6 spends two disks’ worth on dual parity: (n − 2) × size.
    2. Usable = 6 TB
    3. It survives two disk failures.

    Answer: 6 TB; survives two disk failures

  6. Subnet details for a /24 address

    A host is configured as 192.168.157.72/24. Find the subnet mask, network address, broadcast address, usable host range and number of usable hosts.

    Show the working
    1. /24 means 24 network bits, so the mask is 255.255.255.0.
    2. The interesting octet is the third, where the mask is 255. Block size = 256 − 255 = 1.
    3. The network address is the multiple of 1 at or below the address in that octet: 192.168.157.0.
    4. The broadcast is one below the next network: 192.168.157.255.
    5. Usable hosts run from 192.168.157.1 to 192.168.157.254: 2^8 − 2 = 254 addresses.

    Answer: Mask 255.255.255.0, network 192.168.157.0, broadcast 192.168.157.255, hosts 192.168.157.1–192.168.157.254 (254 usable)

  7. Reading permissions as an octal mode

    ls -l shows a file as -r--r-x--x. What octal mode would you pass to chmod to set exactly these permissions?

    Show the working
    1. Ignore the first character (file type). Split the rest into owner, group and others, three characters each.
    2. Score each triple: r = 4, w = 2, x = 1, dash = 0.
    3. owner r-- = 4 = 4; group r-x = 4 + 1 = 5; others --x = 1 = 1
    4. Mode = 451, so the command is chmod 451 file.

    Answer: 451

  8. Keyspace and entropy of a password policy

    A password of 13 characters is chosen at random from lowercase letters (26 possible symbols). How many bits of entropy does it have, and how long would trying every combination take at 10 billion guesses a second?

    Show the working
    1. Entropy = length × log₂(symbols) = 13 × log₂(26) = 13 × 4.7
    2. = 61.1 bits
    3. Combinations = 26^13 ≈ 2.48e+18
    4. Time to try them all = combinations ÷ 10¹⁰ ≈ 7.9 years. On average an attacker finds it in half that.
    5. This only holds for truly random passwords. A human-chosen word with a digit on the end falls to a dictionary attack far sooner.

    Answer: 61.1 bits; about 7.9 years to exhaust

Why these four calculations

RAID capacity decides how much storage you get from the disks you buy and what failure the array can survive. Subnet details matter whenever a server needs a static address, a gateway and a place in the right network. Octal permission modes are how chmod sets access on Linux files. Password keyspace turns a password policy into a number, which helps you explain to managers why length matters more than complexity rules.

Common slips to watch for

With RAID, people often count parity wrongly: RAID 5 costs one disk's worth of space whatever the number of disks, and RAID 6 costs two. Remember too that RAID 5 on many large disks has a long rebuild, during which a second failure loses the array. With permissions, the most common error is mixing up the order of owner, group and others. With passwords, the calculation assumes truly random characters, which human-chosen passwords rarely are.

Common questions

Is RAID a replacement for backups?

No. RAID protects against disk failure only. It does nothing about deleted files, ransomware, corruption or a failed controller, so backups remain essential.

What does chmod 755 mean?

The owner can read, write and execute, while the group and others can read and execute. It is common for directories and scripts that others need to use but not change.

More Systems Administrator guides

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