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Population
Then they butchered large sheep and fat goats, and they butchered fat pigs and a cow from the herd.
Again the suitors will butcher a great amount of animals.
Odyssey Book 20 line 219-220 Barry B Powell
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The reason for this great amount is of course the feast for the people in the city. The meat isn't only meant for the household (Oikos) of 188 people, but for the Polis also. Let's now try to extract the amount of people from this massive butchering.
For the second butchering Eumaios brought 3 pigs to the palace and it is to be expected that he brought the same amount the day before.
Let's use the same amount of sheep and goats and the 2 cows mentioned by Homer to make an estimation.
6 pigs of about 80kg, resulting in 40kg of meat each, is 240kg,
6 goats of about 40kg, resulting in 20kg of meat each, is 120kg,
6 sheep of about 50kg, resulting in 25kg of meat each, is 150kg,
2 cows of about 300kg, resulting in 150kg of meat each, is 300kg,
That brings a total of 610kg of meat.
Let's say that, on average, every inhabitant aged 12 years and older will consume about 0.4kg of meat, than the amount is about 2025 citizens.

This includes the people of the palace who also ate twice, so we have to substract 188 people, leading to 1837 people above the age of 12.

So, now let's make an age composition: Age 0-12 25%, age 12-24 22%, age 24-36 20%, age 36-48 18%, age 48 and older 15%.

This of course does not count for the suitors and their servants, they came young and unmarried and didn't bring any children. So we have to substract 118 from 1837 that is 1719 people.

So this 1719 souls form 75% of the population, so we have to divide the number by 75 and multiply it by 100 to come to the estimated amount of all people in the city which is 2292 inhabitants.

Assuming an average of 7 people in a household there must be about 327 houses in the city.