Imagine a small chess board, 3 x 3. If you place a knight on the top left hand corner, how many different squares can the knight reach in less than 4 moves?
I assume you mean 3 squares by 3 squares. If in 3 moves (3 < 4.), he can go to middle bottom, upper right and middle left — or he can go middle right, left bottom and middle top. Are you assuming just one of these alternatives or both?
To determine how many different squares a knight can reach in less than 4 moves on a 3x3 chessboard, we can follow these steps:
Step 1: Visualize the chessboard and mark the starting position of the knight.
```
a b c
1 ⚘
2
3
```
Step 2: Calculate the number of reachable squares in one move from the knight's starting position.
A knight's move consists of moving two squares in one direction (either horizontally or vertically) and then one square in a perpendicular direction. In this case, the knight can move to positions b2, c3, and c1. These three squares are reachable in one move.
Step 3: Calculate the number of reachable squares in two moves from the knight's starting position.
To find this, we need to consider two types of moves: a move that takes the knight to a square in one move from its current position and another move that takes the knight to a square in two moves. The reachable squares in two moves are marked below.
```
a b c
1 ⚘ ⚋
2 ⚋ ⚕
3
```
Step 4: Calculate the number of reachable squares in three moves from the knight's starting position.
Similarly, to find this, we need to consider three types of moves: a move that takes the knight to a square in one move, a move that takes the knight to a square in two moves, and a move that takes the knight to a square in three moves. The reachable squares in three moves are marked below.
```
a b c
1 ⚘ ⚋ ⚋
2 ⚋ ⚕ ⚋
3 ⚋ ⚋
```
Step 5: Add up the total number of reachable squares in less than 4 moves.
By summing up the marked squares from Steps 2, 3, and 4, we find that the knight can reach a total of 4 different squares in less than 4 moves on a 3x3 chessboard.
Therefore, the answer is 4.