Fermi Estimation (Technical)

How it works

Technical mode is the assessment-style sibling of classic Fermi, modeled on the timed online tests trading firms use. An 8 question round is drawn from curated questions plus a procedurally regenerated pool - the dice boards and grid paths inside it are freshly rolled each visit to the menu. Categories: visual counting, grid path, combinatorics, random walk probability, market microstructure, and hardware latency, each filterable, along with a Warm-up / Interview / Hard difficulty filter.

Answers here sit in a tight numeric band, not a magnitude band - a count of dice, a path length, a latency in milliseconds. You still quote a LOW and a HIGH, but each question carries its own time limit (a 40 second dice count is a different drill from a 25 second calculation), shown as a countdown.

Visual questions render the actual stimulus: a board of dice faces to count, or a labelled path plotted on a grid whose segments you sum mentally. Calculation questions give you the setup and expect a rule-of-thumb computation under the clock.

How scoring works

A range that misses the answer scores 0, as does an inverted range. For a range containing the answer, tightness is measured as relative width: (high - low) divided by the true answer. Within 10 percent of the answer scores 3 (Bullseye), within 25 percent scores 2 (Tight market), within 60 percent scores 1 (Wide but inside), and anything wider scores 0 - a market too wide to be wrong says nothing and is refused, exactly the hedge the scoring exists to punish.

Each question is worth up to 3 points across the 8 question round. Your best technical round total is stored locally, separately from the classic best.

Count in structured passes, not one sweep

On a visual counting board, a single left-to-right sweep undercounts under pressure because your eye loses its place. Instead, partition the board into regions - quadrants or rows - count each region once, and keep a running subtotal per region. Re-checking one suspect region costs seconds; recounting the whole board costs the clock.

Count by recognition, not enumeration. Dice pips are read as faces (that is a five, that is a three), and you are usually counting occurrences of target faces, so the task is really scan-and-tally: fixate, classify, increment. Subvocalizing the tally in groups (3... 6... 9) is measurably steadier than counting by ones.

Your quoted range should reflect your counting confidence. A clean count on a small board deserves a width of one - count 12, quote 11.5 to 12.5 and take the Bullseye band. A crowded board where you may have missed one or two deserves count minus 1 to count plus 2. The relative-width bands mean small absolute answers tolerate almost no slack: 10 percent of 12 is about 1.

Turn pictures into arithmetic

Grid path questions are sums of segment lengths, and the fast method is to accumulate as you trace: read each leg off the coordinates (horizontal and vertical legs are just coordinate differences), add it to a running total, and never look back. Diagonal legs on a grid are the one place estimation enters - a diagonal across a and b is sqrt(a^2 + b^2), and knowing the 3-4-5 and 5-12-13 triples plus "diagonal of a unit square is about 1.4" covers nearly everything.

Calculation categories run on a small kit of rules of thumb: volatility scales with the square root of time, light in fiber covers roughly 200 km per millisecond (two thirds of c), and powers of two up to 2^20 (about a million) handle combinatorics counts. Rehearse the kit before playing; the time limits are set so that deriving a rule from scratch does not fit, but applying a known one comfortably does.

When a formula gives you an exact answer, resist the urge to quote wide out of habit. The scoring rewards recognizing which questions are exact (a computed path length, a power of two) and quoting them nearly degenerate, saving the wide quotes for genuinely perceptual questions.

Quote like a market maker

The labels are not decoration - this is bid/ask discipline. A market maker quotes a spread wide enough to survive being wrong and tight enough to win the trade; here the trade-off is literal: 10 percent relative width pays 3, 25 percent pays 2, 60 percent pays 1, wider pays nothing. Before submitting, ask the two market-maker questions: would I be shocked if the truth were below my low? Above my high? If either answer is no, the range is dishonest in that direction.

Skew the range toward your known error direction. Fast visual counts miss items far more often than they double-count, so skew above your count. Mental sums under time pressure tend to drop terms, so skew high there too. A symmetric range around a biased estimate wastes width on the side you were never wrong on.

Bank the middle band deliberately when the clock is dying. With five seconds left and a rough estimate, a 25 percent range around it scores 2 far more reliably than a hero 10 percent quote scores 3. Across 8 questions, consistent 2s with a couple of 3s beats alternating 3s and 0s.

A worked example

Question type: a plotted grid path A to B to C to D, 40 second clock. Trace and accumulate: A(0,0) to B(3,4) is a 3-4-5 diagonal, running total 5. B(3,4) to C(9,4) is horizontal, length 6, total 11. C(9,4) to D(9,1) is vertical, length 3, total 14.

Two legs were exact coordinate differences and one was a memorized triple, so the answer 14 is exact. Quote 13.5 to 14.5: width 1 on an answer of 14 is about 7 percent relative width - inside the 10 percent Bullseye band for 3 points. Quoting a habitual 12 to 17 would have scored 1.

Common mistakes

• Quoting order-of-magnitude-style wide ranges out of classic-Fermi habit - anything wider than 60 percent of the answer scores 0 even when it contains the truth.

• Recounting the whole dice board after losing your place instead of counting in regions with subtotals.

• Centering the range symmetrically when your method has a known bias - fast counts miss more than they double-count.

• Burning a 25 second calculation window trying to derive a rule of thumb (vol scaling, fiber latency) you should have rehearsed.

• Going for the 10 percent band on a question you only roughly estimated - a missed hero quote scores 0 where an honest 25 percent quote banks 2.

Why interviews test this

This mode mirrors the timed online assessments used by market-making firms such as Optiver, IMC, and Flow Traders: eyeball-counting under a clock, mental sums from a picture, and rule-of-thumb calculations. The format tests calibrated speed - being fast and knowing how accurate your fast answer is.

The bid/ask framing is the culture in miniature. Trading interviews repeatedly ask candidates to "make a market" on an uncertain quantity, then trade against it. A quote that is too wide gets ignored and a quote that is too tight gets picked off; the scoring bands here are that lesson in point form.