Partitioning question

TidBITS Talk
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I want to install Linux on a Mac mini (Note: the mini has its original spinning HD and is running Mojave, slooowly!). I cannot figure out how to create a target partition during installation; what I see does not correspond to the Linux install guide. No matter, I read that one can use Disk Utility to first create the partition (MS-DOS format), then boot from the Linux install disk and select the new partition as target.

So, I open Disk Utility and select “Show All Devices,” which reveals “Apple HDD…–>Container disk1–>Macintosh HD.” I select Macintosh HD, then “Partition,” and choose Partition when Disk Utility presents the Partition versus Volume choice. Then I choose “+” and a 0.5 GB partition appears in the circular map. I obviously want something much larger than 0.5 GB, but Disk Utility will not let me change its size.

Where have I gone wrong? Macintosh HD has 330 GB of unused space. I read elsewhere in TidBITS that live repartitioning of APFS is not possible with DU, but the “create partition first with DU” approach that I read showed Catalina as the example. Do I have to repartition from something like Recovery mode?

Many thanks.

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Update

A clue in another TidBITS thread alerted me to the fact that local Time Machine snapshots can contribute to discrepancy in Finder/Disk Utility reporting of free space. Perhaps a large amount of space was occupied by snapshots that prevented adding a partition larger than 0.5 GB, even though the Finder and DU reported 330 GB of free space.

I checked. There were no TM snapshots (I switched off TM long ago), but there was a 59 GB Carbon Copy Cloner snapshot that I deleted. Voila! It was then possible to create a partition as large as 250 GB (a result that does not make sense mathematically).

But there is a catch. I want an MS-DOS partition, and the only way to get it is to allocate the entire 250 GB to it, leaving no free space for the existing volume. A smaller partition can be created only if it is formatted APFS or HFS. I believe the Linux installer will (re)format the target partition appropriately, but I fear that it will not find the target if it is APFS/HFS.