It is impossible to have a magnet with only a single pole. The North and South poles always exist in unbreakable pairs.
Understand that magnetic strength is concentrated at the poles, and that these poles always exist in unbreakable pairs.
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Explanation of magnetic poles.
Spread iron filings (very small pieces of iron) on a sheet of paper and place a bar magnet over them. If you tap the paper, you will notice something special: the filings do not stick evenly across the magnet.
Visual of iron filings clustered at the poles.

The heavy clustering of iron filings shows that a magnet's pulling force is strongest at its two poles.
Explanation of what happens when a magnet is broken.
It might seem logical that cutting a magnet exactly in half would separate its North pole from its South pole. However, you cannot isolate a single pole.
Flowchart showing a magnet breaking and forming new poles.

Breaking a magnet does not separate its poles; it instantly creates new poles at the break point, resulting in two complete magnets.
Question testing understanding of broken magnets.
If a bar magnet is accidentally dropped and breaks into three smaller pieces, how many total magnetic poles will exist among the pieces?