Practice

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89labs

17tracks

System Design 16

The slate next to the stove

The slate is full and someone asks for something new. Which line gets erased?

5eviction policies

10questions at the counter

1–6lines the slate holds

One wala, many kettles

Sixteen customers, one wala. If the wala stops standing at each kettle, how much sooner is everyone served?

736 → 121 ms16 orders, watched then juggled

384 msthe floor: 64 orders × 6 ms of work

1–4walas, the stall's cores

The order slip rail

The kitchen is 95% busy. How much longer do you wait than at 50%?

99×analytic wait at 99% busy

150×the board's simulated wait at 99%

50–99%how busy you can run the kitchen

Splitting the ledger

Names are mostly A–D. You split A–M / N–Z. What happens?

3shard keys to try

2–6books on the shelf

70names arriving

The bouncer at the door

The limit is 5 a minute. How many can one client land in a two-second span?

4ways to count a limit

10requests in the seam burst

5/minthe board's own rule

The copy clerks

You pay your tab at stall A and walk to stall B. What do they say you owe?

3ways to copy a book

14moments in the evening

1–6moments the clerks run behind

Network partitions

The cut phone line

The line between the branches is cut. What does the far clerk say to the customer in front of them?

3answers to one cut

2–9moments the line stays cut

0conflicts, if you refuse

Charged twice

The reply never arrived. Did the money move, and what should the client do?

3answers to a lost reply

12payments, one evening

0–60%of messages the network eats

Who holds the pen

The room splits in two. Both halves think they are in charge. Who is allowed to write?

5clerks, one pen

3rules for holding it

0diverging writes, with a fence

Distributed transactions

The two ledgers must agree

One transfer, two books, and a crash that lands between them. Where does the money end up?

3ways to move money twice

7moments a crash can land

1protocol that blocks

Choosing a datastore

The right book for the job

Fourteen real queries, six datastores. Which one answers yours without a second system?

14queries, fixed

0stores that win every row

The ledger everyone reads

The same answer is correct under one promise and a violation under another. Which promise did you make?

4promises to a reader

20moments, one evening

0levels that are free

Consistent hashing

The ring

The ring rehomes only 1/N of the keys when a server dies. So why does everyone run two hundred virtual nodes per server?

67% to 6%load spread, 1 to 200 points

765 vs 7,513keys moved, ring against hash % N

1server inherits the hole, at one point each

Thirty stalls on one order

Every stall is slow one time in a hundred. An order that waits on a hundred stalls is slow how often?

1% → 63%one stall late, and 100-stall orders late

26% → 0.30%30 stalls, before and after hedging

+1 in 100extra calls a hedge costs at 1% slow

Counting a crowd

Counting the crowd

A hundred thousand different customers, and a tally board of 12 KB. How far off is its count?

12 KB16,384 tallies, whatever the crowd

0.81%the promised miss: 1.04 ÷ √16,384

8 MBan exact list of a million ids

Many buyers, one item

The last vada

Ten vadas left and a crowd reaching at once. How does the stall sell exactly ten, and what does making sure cost?

2 → 110phantom vadas with no guard, from 2 to 12 buyers per vada

5 per vadawhere checking the count again starts losing to the lock

250 a secondwhat one line hands over, whatever the crowd

AI 10

Tokens and embeddings

One sentence, one tokenizer, a vocabulary you can grow. How many tokens does it cost?

44 → 10tokens, same sentence

425merges, learned in-module

62tokens for 23 characters of another script

The batch size dial

One GPU, one chat, cores 99% idle. How many more chats fit before anything gets slower?

1.07operations per byte, against a ridge of 150

134chats before the cache fills the card

0.7%of the cores busy serving one chat

The temperature dial

The model has read 'The weather today is'. How often does it say something other than sunny?

0.549of the drum misses sunny at T = 1

0.993sunny's share at T = 0.1, nearly greedy

671of 1,000 draws miss sunny at T = 2

The decision threshold

The filter has scored every email. How sure must it be before one goes to the spam folder?

100% to 56%precision, bar at 0.90 then 0.20

0 to 267false alarms per 1,000 good emails, same move

60% to 4%precision at 0.50, spam 1 in 4 then 1 in 100

Mixture of experts

Many experts, one router

Doubling the experts doubles what the model knows and costs nothing per token. So what does it cost?

47B → 13Bknown against computed, at Mixtral's width

0gigabytes saved by any of it

28%of a batch dropped by a collapsed gate

The loop cap

The returns desk's loop keeps asking the model until it answers. How many passes before it hands the customer to a person?

8 of 100answered by the loop at a cap of 1 pass

94 to 96answered, cap 8 then cap 20

$1,611 to $2,285a day at a million conversations, same move

The chunk size

The returns desk cuts its policy into pieces and hands the model the best few. How big should a piece be, and how many should go in?

0 of 7answers arrive whole at 10-word pieces, 3 in the window

4 of 7arrive whole at 25 words, 2 pieces, for 67 tokens

533 tokensto get all 7 at 200-word pieces, 95% not the answer

The learning rate

Every step of training walks the dials downhill. How far should each step go?

29 to 8steps to a loss under 0.01, rate 0.05 then 0.2

8.8 x 10^8loss at step 10 at rate 0.5, up from 33

2.26loss after 200 steps at 0.001, still crawling

Cheap model first, big model on doubt

The cascade threshold

Every request goes to the small model first. How sure must it be before its answer goes out?

94wrong answers in 1,000 get out at the lesson's -1.0 threshold

$0.97per 1,000 requests at -1.0, against $3.00 always-frontier

68wrong answers still out at both 0.50 and 0.80

A small correction beside frozen weights

The LoRA rank

Fine-tuning a 7B model with LoRA trains a small correction beside the frozen weights. How big should the correction be?

4.19 milliontrainable numbers at rank 8 on q and v, 0.060% of 7B

14.07 vs 112 GBmemory to train at rank 8, against a full fine-tune

+0.9quality-proxy points from rank 16 to 256, for 16x the numbers

How Computers Work 8

Memory hierarchy

The memory hierarchy

Same data, same O(n), four access patterns. Why is one of them 31 times slower?

4ways to walk the same data

31×scan vs pointer chase at 64 MB

4–200cycles, L1 to RAM

The interrupt storm

The device taps the CPU on every event. What happens when it taps a million times a second?

233k/swhere taking every tap peaks

0serviced at a million a second

500kthe hybrid still finishes there

Cache line life

You asked for four bytes. Sixty-four arrived. Who paid for the other sixty, and who else wanted them?

16×the traffic, same reads, stride 16

6.25%of each line used, at the floor

11×slower while two counters share a line

Inside a float

Your program stores 0.1. What is actually in those 64 bits?

55decimal places in real 0.1

5.55e-17how far 0.1 + 0.2 misses

2^53where integers go missing

Files and storage

The fsync interval

Your write returned and the power cut a moment later. Is the record on the disk?

0 vs 7,777records lost at one crash, every record vs never

200 → 200,000records a second, every record to never

9.9×faster fsyncing every 10 instead of every 1

Parallel speedup

The parallel ceiling

Ninety-five percent of the job splits across cores. How much faster can it possibly finish?

20×ceiling at 95% parallel

24%of each core used, at 64

10cores before it gets slower

The working set

The program needs twelve pages at once. What happens when it gets eleven frames?

32% → 87%time spent working, 11 frames vs 12

14×more page faults one frame short

+2.3 pointsfrom doubling memory past the working set

Whose turn is it

The time slice

Three long jobs are running when you press a key. How long until the keypress gets the CPU?

800 → 0.05 mskeypress wait, first come vs demote the hogs

2.9 → 500 mskeypress wait, 1 ms turns vs 200 ms

4.3% vs 0.03%CPU lost to swaps, 1 ms vs 200 ms turns

DSA 7

O(1) yaad

A hash map answers in one step, on average. What is the worst case, and when does it start to matter?

276keys, one fixed list

11 vs 3deepest peg, bad hash against good

153probes for the worst lookup at 99% full

Sorting aur searching

Merge sort is O(n log n) and insertion sort is O(n squared). On the list you actually have, which does less work?

5 x 5sorts, input shapes

6.2xO(n squared) beating O(n log n)

35items before n log n wins

How cost grows

A million items. O(n log n) finishes in a blink. How long does O(n²) take?

7rungs on the ladder

10¹²O(n²) operations at n = 1,000,000

6orders of magnitude on the slider

The cliff at n = 11

Ten cities, and you can check every possible route. Eleven, and you cannot. So what do you ship for the eleventh?

181,440tours at n = 10, the last n that finishes

+18.4%the greedy tour's excess at n = 9

1%of n = 12's orders reached before the cap

Dynamic programming

The DP table

The same recursion runs three ways. Which one solves ways(3) fifty-five times, and which solves it once?

465calls to climb 12 stairs

55×ways(3) re-solved, vs once

0calls the table makes

Grab the biggest coin first

The greedy bet

Grabbing the biggest coin that fits gives the fewest coins with 1, 5, 10 and 25. Does it with any coins?

0 of 99amounts greedy gets wrong with 1, 5, 10, 25

3 vs 2coins for 6 with 1, 3, 4: greedy's 4 + 1 + 1 against 3 + 3

24 of 99amounts greedy gets wrong with 1, 3, 4

Keeping the chains short

The short chains

Every find walks a chain of houses up to the root. In the worst order, how long can that chain get, and what keeps it short?

31 hopsthe tallest chain after 31 cables with no habit

5 = log₂ 32the most union by size allows, even on its worst log

52 → 30find steps with path halving, paid for with 45 writes against 31

Mind Blown 6

The 99 percent test

The test is 99% accurate and you tested positive. What are the odds you have it?

9%chance it is real, at 1 in 1,000

18rarities on the dial

3crowds, one test

Selfish routing

The shortcut that slows everyone

The new road is free, instant, and takes nothing away. Why is everybody's drive fifteen minutes longer?

65 → 80minutes, after a free road opens

4,500drivers, where the damage peaks

4/3the worst a road can ever make it

The birthday collision

Twenty-three people and 365 days. Why is a shared birthday a coin flip, and what does that cost you in bits?

253pairs among twenty-three people

20,897short links before it is a real risk

2 bitsto double what you can safely mint

Switching doors

The door switch

You picked a door and the host showed goats behind the others. Should you switch?

2 in 3rounds won by switching, three doors

1 in 2when the host only guesses

3,000rounds replayed at every setting

The fee that compounds

A fund charges 1% a year. How much of your final balance does it take over thirty years?

26%of the balance, 1% over thirty years

$83,557billed, against $198,147 lost

3dials, one fee

Totals that flip

The flipped total

Open surgery wins on small stones and on large stones. How does it lose overall?

78% vs 83%open surgery loses the total

2 of 2stone sizes it wins

182small stones the tube needs to flip it

Game Theory 6

Repeated games

Betraying is the rational move in a single game. How many rounds before staying silent starts to win?

5rounds until cooperation wins

6strategies in the tournament

5–10%mistakes where forgiving beats copying

The second-price auction

It is worth 70 coins to you. What should you write on the slip?

14,520bids swept per rule

0that beat the truth

Credible threats

The empty threat

The incumbent swears it will start a price war if you enter. When should you believe it?

3cost where the threat turns real

4lost by believing an empty threat

1978Selten's chain store paradox

Fight or back off

Hawks and doves

Some birds always fight for food and some always back off. What share of fighters does a population settle at?

V/Cthe share of hawks that lasts

40%hawks at prize 4, injury 10

1973Maynard Smith and Price

The lemon market

Buyers can't tell a good used car from a lemon. How many lemons does it take before good cars stop selling?

20%lemons where good cars start leaving

0good cars sold at 25% lemons

1970Akerlof's market for lemons

Competing sellers

The price war

Two sellers share a market. Does competition between them push the price all the way down to cost?

40price when two sellers choose amounts

10price when two sellers post prices

1883Bertrand's reply to Cournot

DevOps 6

The load balancer

Every algorithm looks identical on the benchmark. Which one is still standing when two requests in a hundred cost sixty times the rest?

2 vs 8backends read, ask-two vs least

7.4s → 2.9sp99 wait, round robin to ask-two

55requests stranded on a dead backend

The two gates

Your packet passed both gates on the way in. Does the answer get back out?

1 vs 2rules for the same conversation

4gates one conversation passes

1024–65535the range that decides if it hangs

The autoscaler lag

Your traffic goes up eightfold in three minutes and the HPA is working perfectly. Who still gets an error?

77%of a launch dropped on two pods

60%of the peak fleet's bill, for the HPA

15–120show long a new pod takes to serve

The restore drill

A backup every night, and someone drops the main table at 11:59 pm. What is the cheapest way to lose under a minute of writes instead of a day?

1 day → 28.8 sdata lost, nightly photos, then with the logbook

$28 → $34.72a month, the price of that logbook

15 min–1 dayhow often the database is photographed

Booking quay space

The berth plan

Each ship books quay space before it docks, and the harbour master trusts the booking. How much should a ship book?

33%of the hour's work squeezed when ships book 100m against a 500m tide

12 of 24ships left at anchor when every ship books 1000m

6.0 coresbooked and idle on average, even at the accurate 500m booking

Cheap servers that can be taken back

The spot share

Spot is 63.6% cheaper than on-demand, and it can be taken back. How much of the fleet should run on it?

$1,471.68 → $535.09ten m7i.xlarge servers for a month, all on-demand against all spot

63.6%the cheapest spot share at a = 0.5, $1,173.65 with spares

0.318the bite below which all spot is cheapest

Finance 6

The minimum payment

You owe 5,000 at 24% a year. What does paying 100, 110 or 250 a month actually buy you?

neverat 100 a month, the interest

122 monthsat 110, and 13,320 paid

26 monthsat 250, and 6,449 paid

Diversification

One cloud, many rivers

Each river swings 20% a year and shares some weather. Own a hundred: how much does your water still swing?

12.17%swing with 10 rivers at correlation 0.3

10.95%the floor, 20% x sqrt(0.3)

7%average flow at every setting

The drought right

A right to buy one barrel of water at 100 in a year, when water costs 100 today. What is it worth, and what makes it worth more?

7.97at 20% volatility, strike 100, one year

15.85at 40%, same strike

0change to the payoff at expiry

The borrowed bucket

Borrow two buckets for every one you own and pour all three into a market averaging 7% a year. Do you end up with more water?

1.75xwhere long-run growth peaks at 20% volatility

-4%long-run growth at 4x

0%of 1x paths sold out

The netting window

Three banks send each other 48 payments in a day. Settle each the moment it is made, or pay only the difference at 17:00?

85%less water moved, netted once at 17:00

4,782promised and unpaid at 17:00

0exposed under gross settlement

The nightly match

Card payouts reach the bank days late, and two payments never arrive. How long should an entry wait for its twin before someone is told?

60false alarms in a month at 0 days, payouts up to 4 days late

0false alarms at 3 days

4 daysthe missing payment hides at 3 days

Networking 5

Subnetting and NAT

One address, many doors

Move the split one bit and the street halves. How many machines fit, and how do they share one public address?

/8–/30where the split can fall

254machines on a /24

64,512doors behind one address

Reliable delivery

The lost page

The post loses one page in ten. What should you send again - and how much does the answer cost?

8xa window of 8 over waiting, at 0% loss

46% vs 75%clean speed kept at 20% loss, gap vs lost page

35 of 97pages binned by go-back-N at 20% loss

Connection setup

The TCP handshake

The pipe is 100 Mbps and the file is 1 MB. Why does the round-trip time decide how long it takes?

4ways to open a connection

1-300 msnext rack to geostationary

1.09xwhat 100x the bandwidth buys

The TTL dial

You changed the address. How long until the world stops sending people to the old one?

125 → 10queries at TTL 5s vs 300s

182sstranded on the dead address

153 → 25 msmean lookup, blink to 5 min

The full buffer

A bigger waiting yard means fewer parcels turned away. Why does it make the whole house feel slower?

40parcels, one round trip's worth: full road

62 vs 552 msping, yard of 40 against 1000

42 msCoDel's ping, whatever the yard

Data Systems 4

Storage engines

LSM vs B-tree

Write-heavy wants an LSM, read-heavy wants a B-tree. Where exactly is the flip?

46.9%read share where the bill flips

3amplifications, each crossing somewhere else

2.85xread cost the bloom filter removes

Isolation levels

Two doctors each check that someone else is on call, both go off call, and both commit. Which level notices?

5races, named as they happen

32operations, one schedule

7transactions interleaved

Stream processing

The late tap

A tap from a phone in a tunnel arrives twenty seconds late. How long should the server wait before showing a count?

12taps, the lesson's own

3thrown away at a 5-second wait

18 sshortest wait that loses none

Failure detection

The heartbeat timeout

A follower sends a heartbeat every second and the leader gives up after some silence. How much silence is enough?

3live followers called dead at 3 s (calm network)

5 sshortest timeout with no false alarm (calm)

13 sthe same, on the busy network

Database Internals 4

The selectivity crossover

Your query has an index and Postgres refuses to use it. At what fraction of the table does reading all of it in order start to win?

1.17%of the table, where the plan flips

62%the same crossover, on SSD costs

2.02×the bill a stale sketch pays

The vacuum lag

One transaction has been open for an hour and nobody noticed. Why is the table three times the size of its data?

6×the table, horizon pinned

0versions a sweep can reclaim

0–20steps the oldest reader lags

Write-ahead logging

The write-ahead log

You checkpoint three times as often for a faster restart. Why does the log get bigger?

2.8×more log at the tight end

29×longer replay, loose end

2–30writes between checkpoints

Query execution

The work_mem dial

Your sort spills to disk. Give it more memory and it stops. Why does nobody set work_mem to a gigabyte?

191 → 0 MBspilled to disk, the default to the whole room

95 MBspilled at 16 MB and at 64 MB alike

50 GBwhat 100 sessions could ask for at 256 MB

How Things Work 4

The overloaded strip

One extension strip, one fuse, one cord. Plug in one more thing. Which fails first?

4xthe heat in a cord when its current doubles

1.85xrated heat in a thin cord, fuse intact, at 8.15 A

16.85 Aadd the kettle and the 10 A fuse blows

The stopping distance

A child steps out where a 50 km/h car would just stop. How fast is a 60 km/h car still going there?

38 km/ha 60 km/h car still has where 50 km/h stops

4xbraking distance for twice the speed

31.5 km/hwhere thinking and braking distance are equal

The heat pump

A fridge and an air conditioner run the same loop. Why does one move twice as much heat per joule?

3.54the ceiling for a fridge's 70 K hill

6.95the ceiling for an air conditioner's 40 K hill

251 Wto warm with 1,000 W, against a heater's 1,000

The muggy night

It is 40 °C. Does a fan help, and does the answer change when the air is wet?

+181 Wto spare with a fan at 40 °C, 60% humidity

-283 Wwith the same fan at 80%: worse than still air

3.4xhow much faster a fan carries heat and vapour

Security 3

The revocation window

You sign a stolen login out everywhere. How long does the thief's copy keep working?

15 mina stolen 15-minute token outlives its revocation

4xrefreshes when the lifetime drops from 60 to 15 min

0 sthe window with a revocation list, read on every request

Password storage

The slow hash

A million password hashes have been stolen. How much does a slower hash actually buy you?

2xlogin time and cracking time for each +1 of bcrypt cost

31,000xbcrypt cost 10 against plain SHA-256, per guess

1,000,000separate searches a salted table forces, one per user

Defence in depth

The chain

An attacker must get through every stage of a breach unseen. How good must each control be?

4.67%finish unseen past six separate 40% controls

64xfewer attackers through at 60% per stage than at 20%

60%get through when all six share one log pipeline

From Scratch 1

Consumer groups

The consumer lease

You start ten consumers against a four-partition topic. How many of them do any work?

10 vs 2partitions stopped, eager against cooperative

4×parallelism at 8 consumers on 4 partitions

1 of 3members range strands on three small topics

Personal Development 1

Procrastination

The deadline curve

The essay is due in 30 days and the phone pays now. On which day does the essay win?

7days left when the essay ties the phone

30 or 60deadline length, same start: a week before

1.60 vs 2today's session loses to friends going out

Philosophy 1

The veil

You must pick a society's rules before you know which of its hundred people you will be. Which do you pick?

6.8points of average A wins by at a floor of 12

40points of floor B protects in exchange

0.1points of average lost where the log chooser flips

Psychology 1

Research methods

The forking paths

A thousand labs test a pill that does nothing. How many publish that it works?

39%of labs 'find' an effect with ten looks at nothing

1 − 0.95ᵏthe chance at least one of k looks is a fluke

48% → 21%real effects caught: planned first vs bar raised for ten looks