Question

What is the minimum size of the state space for an "altered" 24 puzzle (a square puzzle similar to the 8 puzzle but 5 by 5 with 24 tiles instead of 8, normally numbered 24 through 1). In the altered version, you only have the numbers 24 through 3 (there is no number 1 or 2 but there are 3 tiles with the number "3" on them).

Select one alternative:
A)25!/2!
B)25!/4
C)25!/3
D)25!/2
E)25!/3!

Answer 1

The minimum size of the state space for an "altered" 24 puzzle with a 5 by 5 grid and the numbers 24 through 3 (without numbers 1 and 2) can be calculated as follows:

First, let's calculate the number of possible positions for the 24 tiles. Since each tile can be placed in any of the 25 positions on the grid, we have 25 choices for the first tile, 24 choices for the second tile, 23 choices for the third tile, and so on, until we have 2 choices for the 24th tile and 1 choice for the 25th tile.

So, the number of possible positions for the 24 tiles is given by 25 * 24 * 23 * ... * 2 * 1, which is equivalent to 25!.

However, in the altered version of the puzzle, there are 3 tiles with the number "3" on them. This means that for any given position of the 24 tiles, we have 3 choices for placing the tiles with the number "3". Therefore, we need to divide the total number of possible positions by 3!.

So, the minimum size of the state space for the altered 24 puzzle is given by 25! / 3!.

Therefore, the correct option is E) 25!/3!.