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Mathematical overlap number
Calculate the number of participants in each class:

Calligraphy, 600 * 0.72 = 432;

Painting, 600 * 0.85 = 510;

Dance, 600 * 0.80 = 480;

Draw an overlay:

According to the relationship between coincidence, exclusion and total number of people, four equations are listed:

a+b+m = 432

b+c+m = 5 10

c+a+m = 480

432+5 10+480 = a+b+c+3m+600

According to the requirements of the topic, there is no need to find abc, so:

Add up the first three equations and get? 2(a+b+c)+3m = 1422

From the fourth equation? 2(a+b+c) = 1644-6m

Subtract the above two equations and get? -3m = 1644-6m- 1422

M = 74 people

That is, there are 74 people who have participated in all three interest classes.

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Note that there are not at least 74 people, but exactly 74 people.