The Shuttle Puzzle

Arrange 4 each of two kinds of markers (for example, four blue tiles and four red tiles) on the opposite ends of the playing board.

For example: [R] [R] [R] [R] [empty] [B] [B] [B] [B]

The object is to move the blue tiles to the Left and the Red to the right using only slides and jumps.

Slide: a move one square to the right for the red or one square to the left for blue. You must end up in an empty space.

Jump: A move in which red moves to the right by jumping over one blue and lands into an empty space. Vica versa for blue.

Restrictions: You cannot move backwards; for example, you cannot move red to the left or blue to the right. You must always land in an empty space.

1. How many moves does it take to solve the problem?
2. Record the sequence of moves.
3. What is the pattern of moving
4. If N is the # of tiles on one slide of the empty space, what formula could you use to find the # of jumps?

Originally posted by Lord Burn
Arrange 4 each of two kinds of markers (for example, four blue tiles and four red tiles) on the opposite ends of the playing board.

For example: [R] [R] [R] [R] [empty] [B] [B] [B] [B]

The object is to move the blue tiles to ...[text shortened]... empty space, what formula could you use to find the # of jumps?

1. How many moves does it take to solve the problem?
16
2. Record the sequence of moves.
bj = blue jump, rs = red slide etc:
bs, rj, rs, bj, bj, bs, rj, rj, rj, rs, bj, bj, bj, bj, rs, rj, rj, rj, bs, bj, bj,
rs, rj, bs
3. What is the pattern of moving
if N is # of tiles on one side then pattern = s,1j,s,2j,s,3j...Nj,s,(N-1)j,s,(N-3)j,s....1j,s
4. If N is the # of tiles on one slide of the empty space, what formula could you use to find the # of jumps?
N^2

1. How many moves does it take to solve the problem?
It takes 16 moves to solve the problem.

2. Record the sequence of moves.
The sequence of move in order is blue slide, red jump, red slide, blue jump, blue jump, blue slide, red jump, red jump, red jump, red slide, blue jump, blue jump, blue jump, blue jump, red slide, red jump, red jump, red jump, blue slide, blue jump, blue jump, red slide, red jump, and finally a blue slide.

3. What is the pattern of moving?
The pattern of moving is 1 slide, 1 jump, 1 slide, 2 jumps, 1 slide, 3 jumps, 1 slide, 4 jumps, I slide, 3 jumps, 1 slide, 2 jumps, 1 slide, 1 jump, 1 slide, - -in a different view- - s, 1j, s, 2j, s, 3j, s, 4j, s, 3j, s, 2j, s, 1j, s.
So in other words when the pattern is slide, N jump, …, slide. Where N is the number of jumps. In order N is 1, 2, 3, 4, 3, 2, and then 1.

4. If N is the # of tiles on one slide of the empty space, what formula could you use to find the # of jumps?
When N is the # of tiles on one slide of the empty space, the formula could you use to find the # of jumps is N2.

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