Description
[EMERGENCY TRANSMISSION - GALACTIC COMMAND]
Subject: Mission Omega-7 - Navigation through the K-94 Tesseract Anomaly.
Background:
The Omega-7 probe has entered a non-Euclidean hyper-dimensional region known as a Tesseract Grid. The probe’s onboard computer is failing, and you must provide a sequence of movements to reach the "Stability Core" before the probe's energy reserves deplete or it is crushed by a Quantum Anomaly.
1.The 4D Toroidal Spacetime:
The grid is a 4-dimensional hyper-cube of size . Coordinates are given as where . The space is toroidal in all four dimensions: moving from in any direction with a step of results in 0.
2.Goal Decoding (The Eigen-Lock):
The coordinates of the Stability Core are hidden within a 4 x 4 Quantum Matrix M. To decode :
  1. Find the four eigenvalues of .
  2. Take the absolute value of each eigenvalue.
  3. Sort these values in ascending order:
  4. Apply a permutation vector ( where P contains indices 1 to 4) such that
  5. The final coordinates are
3.Dynamic Quantum Anomalies (4D Cellular Automata):
The grid is infested with anomalies. Let be a logical 4D array where means an anomaly exists. The field evolves every second based on the number of neighbors K(where each cell has - 1 = 80 neighbors):
  • Birth: A cell becomes active if it was dead and has exactly B neighbors.
  • Survival: An active cell remains active if it has between and neighbors.
  • Energy Flux: Each active neighbor of a cellB at time t increases the "Action Cost" of moving into that cell by 0.1
4.Space Warping ( The Wormhole Effect ):
There are two special coordinates, and . If the probe enters at time t, it is instantly transported to at time (and vice versa) with a fixed cost of 0.5, regardless of local anomalies.
5.Energy and Action Constraints:
  • Max Energy: The probe starts with .
  • Consumption: Each move (including staying still) consumes 1.0 unit of energy. If , the mission fails.
  • Action Cost: The total "Action" to be minimized is the sum of costs:
  • Movement: In one second, the probe can move to any of its 80 neighbors or stay in place. However, it cannot enter a cell that is currently "Active" at time t.
Goal: Find the minimum total Action to reach steps and before energy runs out.
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Last Solution submitted on Mar 20, 2026

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Hoang Minh Tri

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