*[Editor’s note: This story is republished with permission by Rocky Agrawal. It originally ran yesterday on his blog, reDesign.]*

Quick: How many people bought a Groupon in the third quarter?

The obvious, easy answer based on the latest S-1 is 29.5 million. That’s what Reuters wrote Wednesday. (They rounded up to 30 million.) But that number is wrong.

What Groupon reports in their S-1 (in their quarterly results) is how many people have ever bought a Groupon. Because it is listed in the quarterly section, someone who is not deeply studying the S-1 would assume that that’s how many were sold in the quarter. Groupon intermingles quarterly results and cumulative results in the same column.

This is just one of the many tricks used by Groupon to hide data.

This method of reporting would hide sequential declines in actual purchasers of Groupon during the quarter. It’s possible that fewer people purchased a Groupon during the third quarter than the second quarter. But we don’t know, because Groupon doesn’t tell us.

At times, reading the Groupon S-1 is like solving a GMAT data sufficiency problem. Do I have enough data points to find this information?

So how many people did actually purchase Groupons during 3Q?

- We know that the number of people who have ever purchased Groupons increased by 6.4 million from 2Q to 3Q. So at least 6.4 million people purchased Groupons in 3Q. That would imply that no one who had ever purchased a Groupon before purchased one in 3Q. So that number is clearly too low.
- We know that as of 3Q, 29.5 million had ever purchased a Groupon. If everyone who had ever purchased a Groupon bought one in 3Q, that would mean 29.5 million purchased one. That’s the number Reuters reported. Clearly that number is too high.
- We know that between 2Q and 3Q the number of repeat purchasers increased by 4 million. These are people who had purchased only one Groupon before and then purchased another one, making them a repeat purchaser.

Putting all that together, if you take the number of people who were new purchasers of Groupons (6.4 million) and add in the increase in the number of repeat purchasers (4 million), you end up with 10.4 million.

That number is also high because new customers who bought more than one Groupon in 3Q would be counted twice. We don’t know how many of those there were.

But it’s low because some proportion of people who were already repeat customers in 2Q would also have been repeat customers in 3Q. If we assume that 60% of repeat customers in 2Q bought in 3Q, that’s another 7.2 million. (We don’t know what that proportion is; this is an estimate.) Adding that in, we get 17.6 million.

Is that number exactly right? No, but it’s a better number than the 29.5 million. (The biggest variable is what proportion of 2Q repeat customers repeated in 3Q.)

Groupon could easily report the number of customers who purchased a Groupon in a given quarter. So why doesn’t it? It’s material information. The fact that the company goes out of its way to hide information like this should be a big red flag.

*Rocky Agrawal is an analyst focused on the intersection of local, social and mobile. He is a principal analyst at reDesign mobile. Previously, he launched local and mobile products for Microsoft and AOL. He blogs at http://blog.agrawals.org and tweets at @rakeshlobster.*