The minimum number of people who claimed ancestry from all three heritages is : 45
Given that there are 100 relatives
let's assume that 1 relative = 1 room
100 relatives = 100 rooms
Number of relatives with Italian heritage = 90
Number of relatives with German heritage = 80
Number of relatives with swiss heritage = 75
Step 1 :
Fill up the first 90 rooms with Italian heritage relatives
Fill up the remaining 10 rooms with 10 Relatives with German heritage
Step 2 :
Distribute the remaining 70 relatives with German heritage into 70 rooms out of the 90 rooms already occupied by the relatives with Italian heritage
Step 3:
Distribute the 75 relatives with swiss heritage into the 20 rooms occupied by Italian heritage relatives only and 45 rooms occupied by both German and Italian relatives and into the 10 rooms occupied by the German heritage relatives
Therefore we can conclude that the minimum number of people who claimed ancestry from all three heritages is : 45
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