18.2. Disjoint Group Sums

Try these first

1. 1.

   What is the minimum age sum possible with 9 ages ranging from 18 to 58?

   Hint

   Consider the smallest age in the range.

2. 2.

   What does the pigeonhole principle state?

   Hint

   Think about distributing objects.

3. 3.

   What does the pigeonhole principle help us demonstrate?

   • Guarantee unique groups
   • Guarantee equal sums in groups
   • Guarantee overlap in groups

   Hint

   Think about the basic requirement of pigeonhole.

4. 4.

   True or False: If there are 9 ages, it's possible to have unique sums for each group.

   • True
   • False

   Hint

   Consider limits of age grouping.

5. 5.

   Create a strategy for finding disjoint groups among any set of ages, where you are given distinct ages ranging from a different minimum to a maximum.

   Hint

   Break down ages into pairs and work through combinations.

6. 6.

   If there are 12 students aged 18-60, how would you utilize the pigeonhole principle to confirm shared sum age groups?

   Hint

   Iterate through subsets systematically.