Polya Framework Workshop

Attempt these four tasks before opening feedback. Keep a short contract, plan, argument or trace, and a looking-back note. These are the required P tasks; additional lesson drills are targeted repair or optional enrichment.

P01: State the problem

For [2,2,1,3], specify strict LIS length versus non-decreasing LIS length. Give a valid witness for each and a rule for ties.

P02: Compare plans

For coins 1,3,4 and amount 6, write greedy and exhaustive plans before calculating. State what evidence would refute greedy optimality.

P03: Audit a loop

Prove the lower-bound partition invariant from lesson 3, including empty input and a target above every element. Separate termination.

P04: Look back

For the sum of the first n odd positive integers, compute n=0,1,2,3, conjecture a formula, prove it, and state one transfer with its limit.

Record assistance and reuse relevant lab evidence; do not duplicate the same work to satisfy several checklists.