Venture Capital puzzles, solved step by step

About 381 companies a year. The four pass rates multiply to 0.525%, so only one sourced company in about 190 becomes a closed deal. Working backwards: 2 deals need 2.86 term sheets, 19 partner meetings and 76 first meetings, which need 381 companies in the top of the funnel. That is seven or eight new companies every week of the year.

Why do the pass rates multiply?

Think of a college admission that needs you to clear a written test, then an interview, then a document check. If one applicant in five clears the test and one in four of those clears the interview, only one in twenty of the original applicants is still standing before the document check even starts. Each stage of a funnel acts only on what survived the stage before it, so the overall rate is the product of the stage rates, not their sum or average. Here that product is 0.20 x 0.25 x 0.15 x 0.70, which is 0.00525, or about one company in 190.

How do you say it out loud without losing the room?

Work backwards from the answer the interviewer cares about, one stage at a time, and say each number as you go. Two closed deals at a 70% close rate need 2.86 term sheets; at 15% that is 19 partner meetings; at 25% that is 76 first meetings; at 20% that is 381 companies. Then translate it into a working week: 381 over 52 is about 7.3 new companies a week and about one and a half first meetings a week, which is a concrete picture of the job.

Keep the fractions until the end. If you round up at every stage instead, you get 3 term sheets, 20 partner meetings, 80 first meetings and 400 companies, a 5% overshoot from rounding alone. It is not a disaster, but it shows the interviewer you carry precision until the last step.

What would you add after the number?

Point at the stage with the most leverage. Every rate matters equally in the product, but they are not equally easy to move. Lifting the partner-meeting rate from 25% to 35%, by screening harder before first meetings, cuts the sourcing need to about 272 companies. The limitation is worth a sentence too: real funnels are lumpy, and a fund that closes two deals a year will see years with one and years with four.

About 5 months. Both flows are a share of the same base, so the base grows by 20% minus 5%, a net 15% a month, and that 15% compounds. The rule of 72 gives 72 over 15, about 4.8 months; the exact answer is ln 2 over ln 1.15, 4.96 months. A check: 1.15 to the fifth power is 2.01.

What is the real growth rate here?

Picture a water tank with a tap pouring in and a small leak at the bottom. How fast the tank fills depends on the tap minus the leak, not on the tap alone. When new users and lost users are both a share of the same base, the base grows at the difference between the two rates, here 20% minus 5%, or 15% a month. The 20% is the headline the founder will quote; the 15% is the number that moves the base.

Why is it not 100 divided by 15, about 6.7 months?

Because each month's 15% is taken on a bigger base than the month before. Adding 15 percentage points a month treats growth as a straight line; compounding means month five adds 15% of 1.75 lakh, not 15% of 1 lakh. The base is 1.75 times its start after four months and 2.01 times after five, so it crosses double just before the end of month five. The rule of 72 gets you to 4.8 in your head, which is close enough to say first and refine.

What should you say about the assumption?

Say that you assumed both rates apply to the same opening base each month and stay constant. If churn rises as the app reaches less engaged users, which is common, the doubling time stretches quickly: at 8% churn the net rate is 12% and doubling takes 6.1 months. The flow picture also tells you something the headline does not. Users lost each month grow with the base, so a leak that looks small at 1 lakh users is twice as large in absolute terms at 2 lakh.

16 months. The customer pays Rs 10,000 a month, but at a 75% gross margin only Rs 7,500 of that is left after the cost of serving them. That gross profit is what repays the Rs 1.2 lakh spent to win the customer, and 1,20,000 divided by 7,500 is 16 months. Dividing by revenue instead gives 12 months, which flatters the business by a third.

Why does payback use gross profit and not revenue?

A tea stall that spends Rs 1,200 on a signboard has not earned it back when it has sold Rs 1,200 of tea, because the milk, sugar and gas cost money too. CAC is repaid only by what the customer leaves behind after the cost of serving them, which is gross profit, not revenue. Here the cost of hosting, support and payment processing takes a quarter of each month's Rs 10,000, leaving Rs 7,500 to pay back the Rs 1.2 lakh.

What does 16 months tell an investor?

It says how long the company's cash is tied up in each new customer. A company that grows fast with a 16-month payback consumes cash for well over a year on every customer it adds, so faster growth means a bigger cash need, not a smaller one. Many SaaS investors treat payback under about 12 to 18 months as healthy for mid-market customers, though the benchmark moves with customer size and churn. If this customer stays four years, it leaves Rs 3.6 lakh of gross profit, three times its acquisition cost.

Name the limitation as well. The simple payback assumes the customer never leaves. If 2% of customers churn each month, the average customer takes about 19 months to repay its CAC, because some leave before they have paid back.

Carry is Rs 120 crore, and the fund is 3.0x gross and 2.6x net. The profit is Rs 900 crore less the Rs 300 crore of capital returned, Rs 600 crore. The GP takes 20% of that, Rs 120 crore. LPs receive Rs 780 crore on Rs 300 crore, which is 2.6x, against 3.0x for the portfolio before carry.

What is the carry charged on?

Think of a tutor paid a fifth of whatever a student's marks improve by, not a fifth of the total marks. Carried interest is a share of the profit, so the LPs' own capital comes back to them first and only the gain above it is split. The fund returned Rs 900 crore on Rs 300 crore, so the gain is Rs 600 crore and the GP's 20% is Rs 120 crore. A hurdleA minimum return LPs must receive before the GP earns any carry. This fund has none. would delay the carry but, once caught up, would not change its size at this level of return.

Why is net 2.6x and not 2.4x?

Taking 20% off 3.0x would charge carry on the capital as well as the profit. The gap between gross and net is 20% of the profit multiple, 0.2 x 2.0, which is 0.4 turns, so 3.0x gross becomes 2.6x net. The same logic gives a quick rule: at any gross multiple M with 20% carry and no fees, net is 1 plus 0.8 x (M minus 1). A 2.0x gross fund nets 1.8x; a 5.0x fund nets 4.2x.

What would an LP add?

That fees push net lower still. A typical venture fund also charges an annual management fee on committed capital, often around 2% for the investment period, which reduces both the money invested and the net multiple; confirm the actual terms in the fund's agreement. An LP compares managers on net multiples and net IRR, because that is the only number that reaches its own balance sheet. A GP quoting 3.0x is quoting the portfolio, not the investor's outcome.

Total dilution is 48.8%, not 60%. Each round takes 20% of whatever the holder owns going into it, so the holder keeps 80% each time and the keeps multiply. 0.8 x 0.8 x 0.8 is 0.512, so a founder who started with 100% holds 51.2% after three rounds. The rounds compound in the founder's favour compared with simple adding.

Why can you not add the percentages?

A shop that cuts a price by 20% three times does not sell the item at 40% of the original; each cut is taken on an already reduced price, so it ends at 0.8 x 0.8 x 0.8, 51.2%. Dilution works the same way: each round takes 20% of the stake you hold at that moment, and that stake is smaller every time, so the keeps multiply. After the first round you hold 80%; the second round takes 20% of that, 16 points, leaving 64%; the third takes 12.8 points, leaving 51.2%.

Where does this matter in a real cap table?

Everywhere a founder plans ahead. Because dilution compounds, each later round takes fewer percentage points than the one before even at the same rate: 20 points, then 16, then 12.8. It also means a founder's stake shrinks more slowly than the headline numbers suggest, which is why a founder can raise several rounds and still hold a meaningful share: at 20% a round it takes 7 rounds to fall below a quarter. Rounds of different sizes multiply the same way: a 20% round followed by a 25% round is a total dilution of 40%, not 45%.

One honest caveat: this assumes every holder is diluted equally. Option pool top-ups, anti-dilution protection and investors taking up their pro rata rights all change who absorbs each round, so a real cap table should be built line by line.

About 23.7% after five years and about 5.6% after ten. Each year the company survives with probability 0.75, and the years are independent, so the chances multiply: 0.75 to the fifth is 0.237. Ten years is that number squared, 0.237 x 0.237, about 0.056. Half the companies are gone before the end of year three.

Why do you multiply survival rather than add up the deaths?

Think of a batch of 100 phones, each with a one in four chance of breaking in every year you own it. In year one about 25 break and 75 are left. In year two the 25% applies to those 75, not to the original 100, so about 19 break and 56 are left. A yearly death rate only acts on the companies still alive, so survival shrinks by the same factor each year instead of falling by the same amount. Adding 25% five times gives 125%, and a probability above 100% is the sign you are using the wrong operation.

How do you get 0.75 to the fifth in your head?

Build it from squares. 0.75 squared is 0.5625, call it 0.56. Squared again, 0.56 x 0.56 is about 0.316, which is year four. One more 0.75 takes 0.316 to 0.237 for year five. Year ten is year five squared, so once you have 0.237 the second answer is one step: 0.237 x 0.237 is about 0.056. Saying the squaring route out loud shows the interviewer a method rather than a memorised number.

What does a flat death rate mean for a seed portfolio?

Two more numbers fall out of the same 25%. The average company lives four years, one over the yearly death rate, and half are gone within about 2.4 years, where 0.75 to the n crosses one half. A seed fund of 30 companies with this death rate expects only about 1.7 of them alive at year ten, which is why seed funds are sized for most companies failing. Say the limitation too: real death rates are not flat. They are highest in the first two years and fall for companies that find a market, so a flat 25% overstates late deaths and understates early ones.

Rs 5 crore, which is 10% of the round. Selling 25% for Rs 50 crore values the company at Rs 200 crore after the round. If you sit out, your 10% becomes 7.5%. To get back to 10% you need another 2.5% of a Rs 200 crore company, which costs Rs 5 crore. The general rule: to hold your stake, take the same share of the round as you own of the company.

Why does your stake fall to 7.5% if you sit out?

Think of a pizza cut into ten slices, one of them yours. If the owner adds enough new pizza that the old one becomes three quarters of the total, your slice is unchanged in size but now a smaller share of the whole. A new round does not take shares away from you; it adds shares for someone else, so every existing holder is scaled down by the same factor, here 0.75. Ten per cent times 0.75 is 7.5%, and the other holders' 90% becomes 67.5%.

Why is the answer exactly 10% of the round?

Do the sum, then see the pattern. The round sells 25% for Rs 50 crore, so the post-money is Rs 200 crore and 2.5% costs Rs 5 crore. Taking 10% of the round gives you 10% of the new shares, and you already hold 10% of the old ones, so you hold 10% of everything. This is what a pro rata rightA right, usually written into the investment terms, that lets an existing investor buy a share of a new round equal to its current ownership, so its stake is not diluted. gives an investor: the option to take its ownership share of each new round. It works the same at any round size.

When would a fund choose not to take its pro rata?

The arithmetic says what it costs; it does not say it is worth paying. Rs 5 crore at a Rs 200 crore post-money is a new investment decision at a higher price, and a seed fund with limited reserves may prefer to back a new company instead. The limitation of the clean answer is that it assumes the round stays at Rs 50 crore with your cheque inside it. If your money comes on top of a Rs 50 crore round from others, the round grows and you need slightly more to hold 10%.

The CTO owns 50%, the COO 30% and the CEO 20%. Start with the COO, the person two clues mention. Not owning the least rules out 20. The CTO owning more rules out 50, since nobody can own more than 50. So the COO holds 30, the CTO must hold the 50, and the CEO has the 20 left, which fits the clue that the CEO does not own 30.

Where should you start a puzzle like this?

Seating a dinner table works the same way: you begin with the guest who has the most constraints, because each rule about them removes options for everyone else. Start with the person the most clues mention, here the COO, since two clues bear on the COO and each one deletes a column. Not owning the least removes 20. The CTO owning more than the COO removes 50, because there is no larger stake for the CTO to hold. That leaves the COO at 30 before you have used the third clue.

How do you know the answer is the only one?

There are only six ways to hand three stakes to three people, so you can check them all, but the grid makes it quicker. Once the COO is fixed at 30, the relational clue forces the CTO into the one stake larger than 30, and the last stake goes to the CEO by elimination. Then use the clue you have not used yet as a check: the CEO holds 20, not 30, so it is satisfied. A clue that was never needed to find the answer but still holds is good evidence you have not made a slip.

Say the method as you go. An interviewer giving a one-minute logic puzzle is listening for an order of reasoning, not just the answer, so name which clue you use at each step. The trap is to start with the CEO, because the CEO is listed first, and then guess. One clue about the CEO removes only one cell, so you are left trying cases.

Why would a venture interviewer ask a founders' puzzle?

It is a warm-up that tests clean reasoning under mild time pressure, dressed in the language of a cap table. It also hints at something real: founder splits rarely follow titles, and an investor reading a cap table should not assume the CEO holds the largest stake. The limitation is obvious: real ownership questions are settled by the share register and the shareholders' agreement, not by inference, and the useful skill here is the elimination habit, not the founders.

2,499, then 9,99,996, then Rs 460 crore. The first two use the same shortcut: numbers equally spaced either side of a round number multiply to its square minus the gap squared, so 49 x 51 is 2,500 minus 1, and 998 x 1,002 is 10,00,000 minus 4. The third is a fraction in disguise: 12.5% is one eighth, so halve Rs 3,680 crore three times, to 1,840, 920 and 460.

Why does 49 x 51 come out one short of 2,500?

Picture a square garden 50 metres a side. Take a one-metre strip off the bottom, 50 square metres, and lay it along the right-hand side. It only fits for 49 metres, so one square metre is left over. A rectangle 49 by 51 is a 50 by 50 square with one corner square missing, so the product is 2,500 minus 1, or 2,499. The same picture works for any pair spread evenly around a round number: the product is the middle number squared minus the gap squared.

How do you take 12.5% of anything in a few seconds?

Recognise the fraction first. 12.5% is one eighth, and dividing by eight is the same as halving three times, which is easier to do aloud than any long division. Rs 3,680 crore halves to 1,840, then 920, then 460. Keep a short list of these anchors ready: 12.5% is an eighth, 37.5% three eighths, 16.7% a sixth, 6.25% a sixteenth. Interviewers who give percentage questions usually pick one of them, because the speed of recognising the fraction is what they are testing.

What is the interviewer actually checking?

Speed sets are less about arithmetic than about whether you look for structure before you calculate. Saying the shortcut out loud, square minus one, or halve three times, shows a method that will also work on the next question. Two habits help. Check the size of your answer against an anchor: 49 x 51 must sit just under 2,500. And say the number back with its units, Rs 460 crore, not just 460. The limit of these tricks is that they only work on numbers chosen to suit them; for awkward numbers, round and say so.

Investor B, at 2.68x against 1.32x. Expected multiple is each outcome times its chance. A gets 0.4 x 3 from winners and 0.6 x 0.2 from losers, 1.32x. B gets 0.1 x 25 and 0.9 x 0.2, 2.68x. B is wrong nine times in ten but its winners are big enough to carry the portfolio; A's winners need to be 6.4x to draw level.

Why does the investor who is usually wrong do better?

A shopkeeper who makes a small profit on four sales in ten and a small loss on the rest earns steadily but slowly. A fisherman who comes back empty nine days in ten but lands one huge catch on the tenth can still earn far more. In venture the size of the winners matters more than how often you win, because losses are capped at the cheque while winners are not. A's high hit rate buys only 1.20x from winners; B's one-in-ten rate buys 2.50x.

How far would either number have to move to flip the answer?

Solve for the break-even, because it tells you how robust the answer is. A's winners would need to return 6.4x, more than twice their 3x, to draw level, while B's hit rate could fall from 10% to 4.5% before B dropped to A's 1.32x. B's lead survives a large error in its hit rate, which is why venture investors talk about the size of possible outcomes before the chance of success: an investment that cannot return 25x cannot carry a portfolio like this.

What does the average hide about investor B?

Variance. With 20 investments and a 10% hit rate, B finds no winner at all 12% of the time and returns 0.2x. One winner is enough to lift B's 20-company portfolio to 1.44x, above A's expected 1.32x, so B's result depends heavily on whether it lands at least one outlier. That is the case for venture portfolios of 25 or more companies, and the limitation of the clean comparison: a fund with too few bets can follow B's strategy correctly and still lose money.