Instead of all the incessant “only a genius can solve this” type posts, which can be easily solved if you know the mathematical order of operations,  I thought I’d share a simple maths puzzle which seemed to confuse a start-up I was helping yesterday. I totally understand why, and I simply helped them understand the correct answer.

It is a very simple piece of math(s), and if you’ve had any involvement with investments you’ll know the answer intuitively. I share it simply to illustrate that when/if I assume that a new entrepreneur understands this, I am at fault in my assumption. I try not to assume, I check and explain as necessary.

Two founders start a business, each with 50% of the equity. They raise three rounds of equity funding, for new equity, and each round is for 20% of the Company’s equity. The rounds are discrete, different investors, increasing in value and spaced apart by a number of months. There are no outside parties taking a cut, no options or warrants are issue as part of the process. They are simple transactions.

After these three rounds, how much equity do each of the founders hold, and how much do each of the investors hold? For these purposes I’ll refer to them as Founder 1 & 2, and Investor 1, 2 & 3.

You can understand why my founders believed they’d each hold 20% each.

As this is the Internet, you can rule out any extraordinary events – the business is healthy, the founders are still happy to work together, neither loses their equity in a divorce (or any other of those possibilities I can just hear someone suggesting)!

One of my favourite books of the 1990s is Innumeracy by John Allen Paulos, which contains a similar (simpler) puzzle – if I reduce the price of an item by 50% and then by 50% again, why is it not free as a significant proportion of people interviewed Paulos believed?

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