Here’s a quick sliding puzzle to get your brain pumping. See if you can separate the light and dark counters in as few moves as possible!
Start by drawing a square grid, four squares wide and four squares tall. Make sure the squares are larger than your counters.
The aim is to separate the counters, so all the black counters are on one side of the grid, and all the white counters on the other side.
This type of puzzle is known as a sliding block puzzle. One nice thing is that it’s always possible to solve. No matter what moves you make, you can always find a solution. If you think you’ve really messed up, you can always take all your moves backwards and get back to the start.
The Maths by Email team don’t know the quickest answer, but we can estimate. If you remove all the light counters from the board, it takes eight moves to get the dark counters to one side. If you’re just using the light counters it’s a bit quicker – it only takes five moves to get to the other side. So the solution must take at least 13 moves. We can further estimate that it will take twice that many moves, as half the moves will be opposing up and down, or side to side. So a solution of 26 moves sounds plausible.
After several attempts, our best solution took 27 moves. We think this is pretty good, but there might be a better solution out there. If you find one, let us know!
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