A joke: "there are 10 kinds of computer programmers: those that understand binary, and those that don't"

There isn't really an answer. It's somewhere between 1 and N.

However, you can think about it from a profit perspective.

For example, in marketing one uses segmentation, which is much like clustering.

A message (an advertisement or letter, say) that is tailored for each individual will have the highest response rate. A generic message tailored to the average will have the lowest response rate. Having say three messages tailored to three segments will be somewhere in between. This is the revenue side.

A message that is tailored to each individual will have the highest cost. A generic message tailored to the average will have the lowest cost. Three messages tailored to three segments will be somewhere in between.

Say paying a writer to write a custom message costs 1000, two cost 2000 and so on.

Say by using one message, your revenue will be 5000. If you segmented your customers into 2 segments, and wrote tailored messages to each segment, your response rate will be higher. Say revenues are now 7500. With three segments, a slightly higher response rate, and your revenues are 9000. One more segment, and you're at 9500.

To maximize profit, keep segmenting until the marginal revenue from segmenting equals the marginal cost of segmenting. In this example, you would use three segments to maximize profit.

Segments  Revenue  Cost  Profit
1         5000     1000  4000
2         7500     2000  5500
3         9000     3000  6000
4         9500     4000  5500

There isn't really an answer. It's somewhere between 1 and N.

However, you can think about it from a profit perspective.

For example, in marketing one uses segmentation, which is much like clustering.

A message (an advertisement or letter, say) that is tailored for each individual will have the highest response rate. A generic message tailored to the average will have the lowest response rate. Having say three messages tailored to three segments will be somewhere in between. This is the revenue side.

A message that is tailored to each individual will have the highest cost. A generic message tailored to the average will have the lowest cost. Three messages tailored to three segments will be somewhere in between.

Say paying a writer to write a custom message costs 1000, two cost 2000 and so on.

Say by using one message, your revenue will be 5000. If you segmented your customers into 2 segments, and wrote tailored messages to each segment, your response rate will be higher. Say revenues are now 7500. With three segments, a slightly higher response rate, and your revenues are 9000. One more segment, and you're at 9500.

To maximize profit, keep segmenting until the marginal revenue from segmenting equals the marginal cost of segmenting. In this example, you would use three segments to maximize profit.

Segments  Revenue  Cost  Profit
1         5000     1000  4000
2         7500     2000  5500
3         9000     3000  6000
4         9500     4000  5500