PRACTICE GUIDE WINCENT
Wincent Online Problems: what the test is, and how to train for it
The Wincent online problems screen is 16 questions in 45 minutes - about 2.8 minutes each - answered by typing the number, with no calculator. There is no negative marking, so leaving an item blank gains you nothing over guessing.
Where it sits: Online problem set. The practice sitting on this page runs the same item count, the same clock and the same marking rule, with questions generated by Outcry rather than taken from Wincent.
Outcry is not affiliated with Wincent and has no access to their assessment content. This guide describes an assessment format that candidates report publicly; the questions here are generated by Outcry and are not Wincent’s own.
What it screens
A crypto market maker running high-frequency trading strategies across digital-asset exchanges.
- ✓Expected value computed fast and used to make a decision
- ✓Conditional probability and Bayes updates without formal notation
- ✓Ranking likelihoods rather than computing them exactly
- ✓Fermi estimation: decomposing an impossible question into three easy ones
Where it sits at Wincent
This is the whole sitting rather than one section of it: 16 items in 45 minutes, on one clock.
There is no going back. You answer or skip, and the next item loads, which means the decision to leave an item is final at the moment you make it.
The format
These are the numbers the Wincent sitting on this site runs on, matching the format candidates report.
| Questions | 16 |
|---|---|
| Time | 45 minutes |
| Per question | 2.8 minutes |
| Negative marking | No |
| Answer style | Typed numeric answer, no calculator |
| Where it sits | Online problem set |
What it tests, with a worked example
Every example below is generated by Outcry, drawn from the same question generators the timed drills run. None of them is Wincent’s.
Conditional probability
Bayes' rule in disguise: a test result, a signal, a drawn card, and what it implies.
Example
Roll a fair die until every face has appeared at least once. What is the expected number of rolls?
Answer 14.7
Coupon collector: 6·(1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6) = 14.7.
Counting and combinatorics
Arrangements, selections and the complement trick that turns a hard count into an easy one.
Example
A deck has 11 ranks with 5 cards of each rank, 55 cards in all. You are dealt 5. How many different 5-card hands contain exactly four cards of one rank and one card of a different rank?
Answer 2750
Product rule again. Pick the repeated rank 11 ways, pick four of its 5 cards C(5,4) = 5 ways, then the loose card is any of the 50 cards outside that rank. 11 x 5 x 50 = 2,750.
Estimation under uncertainty
A number nobody knows exactly, reasoned to the right order of magnitude out loud.
Example
4 crates arrive at a receiving dock holding spacers, shims, gaskets and bolts, one content each. Each crate carries a label naming one of those 4 contents, no two labels the same, and every label is on the wrong crate. Opening a crate shows what is in it. How many crates must be opened, in the worst case, to relabel all 4 correctly?
Answer 2
The label-to-contents map is a permutation with no fixed point, and there are 9 of those on 4 items. Opening a crate reveals its contents and splits the live set; picking the next crate after seeing the last result, a minimax search over every opening order gives 2 as the worst case. With 4 = 3 the two possible arrangements are the two rotations, and one look separates them. The general pattern: the last two crates settle themselves only when the two contents left both clash with their own labels.
Ranking outcomes
Ordering several events by likelihood, where only the exact order scores.
Example
An index fund charges 5 basis points a year and keeps 3.0% of assets in non-interest-bearing cash. The index returns 6.0% over the year. What is the tracking difference in basis points, as a signed number?
Answer -23
Tracking difference is the fund's return less the index's. The invested 97.0% earns the index return and the cash earns nothing, so the drag is 3.0% x 6.0% = 0.1800%, or 18.00 basis points. The fee takes another 5 basis points. Together the fund returns 6.0% - 0.05% - 0.1800% = 5.7700%, a tracking difference of -23.00 basis points. Cash drag hurts in a rising market and the fee is the only part that costs the same whatever the market does. Tracking difference is the realised gap; tracking ERROR is the volatility of that gap and is a different number.
Waiting times and repeated trials
How long until the first success, and why the answer is rarely the average you expected.
Example 1
How many digits does 50! have?
Answer 65
Stirling: log10(50!) ≈ 50·log10(50/e) + ½·log10(2π·50) = 63.23 + 1.25 = 64.48, so 65 digits.
Example 2
How many observations are needed for a 95% confidence interval of half-width 2.5, when the standard deviation is 25?
Answer 385
n = (1.96σ/w)². Call it 2: (2 × 25/2.5)² = 400, which overshoots by 4%.
Example 3
A trading floor has 40 people on it. What is the chance that at least two share a birthday, as a percentage?
Answer 89
There are C(40,2) = 780 pairs, each matching with probability 1/365. P(none) ≈ e^−2.14 ≈ 0.12, so about 88%.
Reading the question exactly
At least, exactly, and given that - the three phrases that change the answer entirely.
Example
A puts in 3,000 for 4 months and B puts in 13,000 for 9 months. They clear 33,000 of profit. What is A's share?
- 16,500
- 10,153.85
- 6,187.5
- 3,069.77
Answer 3,069.77
Profit follows capital multiplied by time. A contributes 3,000 x 4 = 12,000 and B contributes 13,000 x 9 = 117,000, so A takes 12,000 / 129,000 of 33,000 = 3,069.77.
What a good score looks like
On a paper of 16 questions with no penalty for a wrong answer, the only thing an unanswered question can do is cost you. Probability rounds are usually marked as part of a wider battery, so a standalone threshold is rarely reported. Where candidates do describe one it clusters around getting two thirds of the items right, with the caveat that these sections are short enough that two mistakes move you a long way.
How to train for it
- 01Work the standard results until they are recall, not derivation: complement, conditional, binomial mean and variance, geometric expectation.
- 02Practise setting up before calculating. Most wrong answers on these are a correct calculation of the wrong quantity.
- 03Do them timed. A probability question you can solve in four minutes and the paper gives you ninety seconds for is a question you cannot solve.
TRAIN IT HERE
The drills that match each section
Likelihood Ranking
Order events from most to least likely - the exact screen-question format.
Fermi Estimation
Piano tuners in Chicago, atoms in a body - scored on order of magnitude.
Quitters Never Lose
A casino stopping-strategy game that is secretly a martingale lesson.
Tail Risk
Rare events and fat tails, and what they do to a plain expected-value estimate.
SIT THE FULL BATTERY
All the sections back to back on one clock, marked the way the real screen marks them, with a by-skill breakdown at the end. Included with any pass.
Also reported at Wincent
Common questions
- Is the Wincent online problems test multiple choice?
- Typed numeric answer, no calculator. You type the number, so there is nothing to eliminate your way to.
- How long is the Wincent online problems test?
- 16 questions in 45 minutes, which is about 2.8 minutes each.
- Is there negative marking on the Wincent online problems test?
- No. A wrong answer costs nothing beyond the mark you would have earned, so leaving an item blank is never better than guessing at it.
- How do I practise for it free?
- Every drill linked on this page is free to play, with no account, inside a daily run cap. Questions are generated fresh each run, so there is nothing to memorise between attempts. The full Wincent Online Problems sitting puts the sections back to back on one clock.