Exercise 1: Hand-Tracing TwoSumBruteForce on [4, 1, 8, 3], Target 11 — Possible Solution
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THE TRACE, PAIR BY PAIR, IN THE ORDER THE ALGORITHM ACTUALLY CHECKS THEM
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list = [4, 1, 8, 3] (indices 0, 1, 2, 3), target = 11

Following the pseudocode's own nested loop order (i from 0 to n-1,
j from i+1 to n-1):

  (i=0, j=1): list[0]+list[1] = 4+1 = 5   -> not 11, continue
  (i=0, j=2): list[0]+list[2] = 4+8 = 12  -> not 11, continue
  (i=0, j=3): list[0]+list[3] = 4+3 = 7   -> not 11, continue
  (i=1, j=2): list[1]+list[2] = 1+8 = 9   -> not 11, continue
  (i=1, j=3): list[1]+list[3] = 1+3 = 4   -> not 11, continue
  (i=2, j=3): list[2]+list[3] = 8+3 = 11  -> MATCH, return (2, 3)

FINAL RESULT: (2, 3)

WHY THE ALGORITHM STOPS EXACTLY HERE
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The pseudocode returns immediately the moment it finds a match, rather
than continuing to check any remaining pairs - since (2,3) is checked
sixth (the very last possible pair for a 4-element list, since there
are exactly 6 pairs total for n=4: 4 choose 2), the algorithm happens
to check every single pair before finding this particular match,
demonstrating the true worst case for this specific input.

WHY THIS WORKS AS AN ANSWER
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The trace lists every pair actually examined in the exact order the
nested-loop pseudocode visits them, shows the sum computed at each
step, and correctly identifies the exact pair (and its position in the
checking order) where the match occurs, rather than skipping ahead to
just the final answer.