Question 54
A photographer must take photographs of 10 members of one family. Each of the 45 pairs of family members must appear together in exactly one photograph. Only photographs containing 2 or 3 people are allowed.
a) Prove that every family member must appear in at least one two-person photograph.
b) Prove that at least 19 photographs are required.
c) Give a distribution of people among 19 photographs satisfying the conditions.
a) Prove that every family member must appear in at least one two-person photograph.
b) Prove that at least 19 photographs are required.
c) Give a distribution of people among 19 photographs satisfying the conditions.