# 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
println(Sols).
```