Sliding Bus Puzzle

'Move yourselves around on the sliding bus, solve the puzzle and make sense of linear sequences' 

On the ‘sliding bus’ you can only change places by moving into an empty space that is next to you. You need to move from the seat in one corner to the seat in the opposite corner and the only space is in one of the other corners! How many moves will it take? This is a good puzzle you can solve by making the bus yourselves in the classroom and moving yourselves around. Investigate what happens as the bus gets bigger and look at the different types of moves you need to make to understand the algebraic structure of the problem.

The video below gives you a quick idea of what is coming! (High speed video!)


This  Sliding bus puzzle worksheet can be used to start and record activity and teachers can read more about the problem in the  Sliding bus puzzle teacher notes.

Problem Outline

In the following puzzle, the aim is to move the yellow counter (bottom left corner) into the space in the top right hand corner in as few moves as possible. The only moves allowed are horizontal or vertical slides into an empty space (there is only one empty space)

What is the fewest number of moves with which this can be achieved? What would the answer be for a 4 x 4 grid?
Investigate this problem….


  • Make a 3 x 3 sliding bus, sit eight people down in the right places and see how many moves it takes to move someone between opposite corners. Remember the aim is to find the smallest number of moves.
  • Now do the same with a 4 x 4 a 5 x 5 and maybe a 6 x 6.
  • You might continue with counters from here, following the instructions on the worksheet.
  • Try to predict the number of moves for the next size grid.
  • Try to generalise about this situation
  • Break the problem down in to different types of move.
  • Change/Extension
  • What happens when…
  • The first space is in a different place?
  • The finishing place is different?
  • The bus is rectangular?
  • The bus is triangular?

Doing it your way

We know from experience that most teachers will add something of their own to a good activity and would love to collect suggestions from users. Please add a comment below or e-mail the author, with any suggestions/additions about how you ran this activity with your class. We will add some of the suggestions people make here.

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