Over to you

16 Dec 2023

Puzzle: Trauma Team bomb defusal #2

One of my kids has gotten into the old Nintendo Wii game Trauma Team, part of the Trauma Center series by Atlus. It’s much easier and less action-oriented than the previous games — New Blood and Second Opinion, and more of a visual novel game for the most part, where the previous games involved quite difficult action-puzzling and strategy in real time.

There’s a section of the game where a series of bombs are placed, with puzzle hints left behind for disarming each bomb. Bomb number #2 has the following clues:

"The sum of the first four is five.
They are led by the largest.
The sum of the last four is eleven.
The smallest leads.
What are they?"

For fun, I wrote a Picat program to enumerate all possible solutions to the puzzle: 24 in total. This is obviously not good enough, but then exploring the scene in the game reveals another crucial clue: the only digits used in the disarming code are 1, 2 and 3. This small refinement immediately reduces the number of solutions to 1. Here’s the code:

% Benchmark 1: picat trauma_team.pi
% Time (mean ± σ):      13.2 ms ±   0.8 ms    [User: 4.6 ms, System: 8.8 ms]
% Range (min … max):    11.4 ms …  15.5 ms    181 runs

import cp.

main =>
  Nums = [A,B,C,D,E,F,G,H],   % 8 digits
  Nums :: 1..3,               % only digits 1, 2 and 3 are used
  sum([A,B,C,D]) #= 5,        % the sum of the first four is five
  max([A,B,C,D]) #= A,        % they are led by the largest
  sum([E,F,G,H]) #= 11,       % the sum of the last four is eleven
  min([E,F,G,H]) #= E,        % the smallest leads

  Sols = solve_all([], Nums), % what are they?
  Sols.len = 1,               % there should only be one solution