18.2.2. Achieving Disjoint Groups

Try these first

1. 1.

   Define a subsequence?

   Hint

   What does it mean to retain the order within a sequence?

2. 2.

   Provide an example of a strictly increasing sequence.

   Hint

   Think of a sequence where every number increases.

3. 3.

   What defines a subsequence?

   • It's a consecutive sequence from a parent sequence
   • It's any selection from a sequence
   • Only distinct numbers form a valid subsequence

   Hint

   Focus on how order is maintained in selections.

4. 4.

   True or False: Every set of n+1 distinct numbers can form disjoint groups with the same sum.

   • True
   • False

   Hint

   Consider how subsets could overlap.

5. 5.

   Given a list of ten distinct real numbers, demonstrate how to find a strictly increasing or decreasing subsequence of length five.

   Hint

   Look for numbers that maintain their order during selection.

6. 6.

   Assume you have six distinct real numbers between 1 and 10, find pairs ensuring that shared values from any disjoint subsets yield the same sum.

   Hint

   Focus on the combinations that lead to shared outcomes.