India's Kumbh Mela festival is usually described as the world's biggest gathering.
Driven by a belief that a dip at the confluence of the Ganges, the Yamuna and the mythical Saraswati rivers on auspicious days will cleanse sins and help bring salvation, millions of Hindus come to the festival in the city of Allahabad every 12 years.
But the turnout of pilgrims on Monday, put out by the civilian administration, is sharply different from the estimate of the festival's top police official, Alok Sharma.
The festival is managed by thousands of state officials led jointly by a magistrate in charge of the civilian administration and a senior police officer in charge of troops.
"According to my estimate, there were only 1.5 to 1.8 million people on the opening day," says Mr Sharma.
He should know: he was in charge of the 2001 Kumbh Mela in Allahabad, and the 1998 and 2010 festivals in Haridwar too. He not only has experience on his side, but also help from rough counts that some of the 8,500 policemen under his charge are tasked to do.
Mr Sharma says his men follow two methods to count crowds at the festival on auspicious days. The count is aimed at estimating the number of people coming into Allahabad to help maintain law and order.
One method involves counting people using the seven major roads leading into Allahabad, assuming that everyone is heading for the Kumbh Mela.
A 10-metre stretch is marked on each of these seven roads, and the number of people passing through each stretch every minute is counted.
Mr Sharma says logistical difficulties mean that police cannot count people coming along the lanes and by-lanes of the city which, he reckons, "accounts for about 30% of traffic" at the festival.
The second method - essentially cross-checking the numbers thrown up by the first method - involves counting people after they have poured into the heavily-guarded festival ground.
"There are three main roads from Allahabad city into the festival ground and we follow the same counting method," says Mr Sharma.
Pilgrims using the pontoon bridges over the Ganges to come to the festival were not counted on the opening day, he adds.
Combining the two methods and the number of people who got off trains at the Allahabad railway station led Mr Sharma to come up with an estimate of 1.5 to 1.8 million people at the festival on Monday.
"A real count is very, very difficult. And there is a tendency to increase the estimate," says Mr Sharma.
Is there any way of counting a close-to-precise number of people at such festivals?
"At the Kumbh Mela in Haridwar (another north Indian city where the Kumbh also happens) in 2010, we tried satellite imagery to count. That gave us a combined figure of 16 million pilgrims for the two busiest days of the festival. But it didn't look like a very realistic figure. I was not impressed by it," says Mr Sharma.
What was the difference between the satellite-fed number and Mr Sharma's "manual" calculation?
"Just half or eight million," he said, hinting at the possibility of a huge margin of error.
So who put out the official count of a gathering of eight million people at the festival on Monday?
Hari Narayan Singh, an assistant superintendent of police, was in the control room that oversees the running of the festival that day. He kept in touch with observation towers near the bathing area throughout the day.
His last count of the day, at 19:00 India time [13:30GMT], was eight million, which he relayed to higher authorities, who informed the media.
How did Mr Singh's colleagues count?
"We first estimate, visually, the number of people going in and out of the water every minute. Then we calculate for the hour and add up for the day. I was here at 2001 too, and we have an idea from those figures too," he said.
So there's really no way of ensuring that wild miscalculations don't take place?
"No, there's no real science to it," said Mr Singh.
Six years ago on the opening day of the Ardh Kumbh festival - an Ardh (or half) Kumbh is held every six years - in Allahabad I had asked the senior-most police officer for his estimate of the gathering.
He had thrown back the question casually: "How many do you think are here?"
Taken aback, I had mumbled that it could be three million or so.
"That's good, I'll go with it," he had said.
The figure came back to me through reports.