1. In the graph below, fill in the table with YES or NO to indicate if the following are walks, trails, paths, cycles or circuits. LOOK AT THE VERTICES AND EDGES. VI VERTICES V1 V2 V3 V5 V6 V3 V1 V2 V3 V4 V3 V5 V2 V3 V4 V5 V3 V6 V2 V2 V3 V4 V5 V6 V2 V₁ V2 V₁ V₁ V2 WALK V6 V3 TRAIL V4 V5 PATH CYCLE CIRCUIT

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Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.