What's new

Swap the blocks

By David, 26 May 2021 Activity

Six squares drawn in a grid, two end squares are coloured, one red, one blue. There are tiles on five of the six squares.

See if you can slide the coloured counters to their matching boxes!

Here’s a puzzle that’s easy to set up, but surprisingly tricky to solve. See if you can swap two counters just by sliding them!

You will need

  • Paper
  • Textas
  • 1 red counter
  • 1 blue counter
  • 3 white counters

Tip: If you don’t have any counters, you can use small pieces of paper and colour them with textas.

Setup

  1. Drawing a rectangle on paper with pen.On your paper, draw a rectangle about 15 centimetres wide and 10 centimetres tall.
  2. Draw a line across the middle of the rectangle, cutting it in two.
  3. Drawing a grid in the rectangle 2 by 3 squares. Six squares in total.Draw 2 lines down the rectangle, dividing it into 6 squares. Don’t worry if the squares aren’t perfect!
  4. Colour the top left square red.
  5. Drawing of six square grid, the two end squares are coloured, one red, one blue.Colour the bottom left square blue.
  6. Put a blue counter in the red square and a red counter in the blue square.
  7. Six squares drawn in a grid, two end squares are coloured, one red, one blue. There are tiles on five of the six squares.Leave the top right square empty, and put a white counter in the remaining three squares.

 

The game

  1. Six squares drawn in a grid, two end squares are coloured, one red, one blue. There are tiles on five of the six squares.Six squares drawn in a grid, two end squares are coloured, one red, one blue. There are tiles on five of the six squares.The goal of the game is to have the blue counter in the blue box and the red counter in the red box at the same time.
  2. Moving a tile on the grid by sliding it to an empty space.To make a move, slide a counter into an empty box from a neighbouring box.
  3. Arrows showing that you cannot move diagonally or jump over a tile.Counters can only go up, down, left or right. They can’t go diagonally, and they can’t jump over other counters.
  4. After you’ve done it a few times, try counting your moves. See how small you can get that number!

 

What’s happening?

Here are some hints that might help you think about this puzzle.

Since there’s only one empty space, the counters seem to follow each other around the board. The next move will put a counter in the spot that just got emptied!

When the empty space is in a corner, you only have two options, and one of them is to undo your last move! The most important moves are when the gap is in the middle 2 squares.

You might notice that the counters seem to move in circles. You can get them to circle around in the 4 squares on the left, or the 4 squares on the right, or a big circle around all 6 squares.

You might notice the red and blue counters following each other. To solve the puzzle, you’ll need to swap the order that they are in. You might want to split them apart and then move them back together in a different way.

If you solve the puzzle but don’t know how, try again. After a few goes, you can try counting your moves to see how quickly you can do it. Anything under 30 moves is pretty good. Our top score was just 18 moves!

Real-life maths

If you find sliding puzzles really hard, you’re not alone! Mathematicians categorise the puzzles as PSPACE-complete, which means that even computers can find it challenging to come up with a solution. Sliding block puzzles take more time for a computer to solve than Sudoku, but they aren’t as hard as a game of chess.

If you’re after more science activities for kids, subscribe to Double Helix magazine!

Subscribe now! button

1 comments

  1. Once you know the trick to swapping the two counters, sliding puzzles become really easy. I usually solve all but the last two rows of a sliding puzzle and then slowly use this technique to get the last two rows solved together.

    ….

    ….

    SPOILER ALERT – The 18 move solution (maybe one of the 18 moves solutions?) is as follows

    The following directions tell you which counter to move. For example, if the letter is “R” then move a counter to the right – since there’s only one counter that can move right, then that’s the one to move.

    R, R, U, L, L, D, R, U, R, D, L, L, U, R, D, R, U, L

      Reply

Leave a Reply

By posting a comment you are agreeing to the Double Helix commenting guidelines.

This site uses Akismet to reduce spam. Learn how your comment data is processed.