umask is a mask, it’s not a subtracted value. Thus:

• mode 666, mask 022: the result is 666 & ~022, i.e. 666 & 755, which is 644;

• mode 666, mask 021: the result is 666 & ~021, i.e. 666 & 756, which is 646.

Think of the bits involved. 6 in a mode means bits 1 and 2 are set, read and write. 2 in a mask masks bit 1, the write bit. 1 in a mask masks bit 0, the execute bit.

Another way to represent this is to look at the permissions in text form. 666 is rw-rw-rw-; 022 is ----w--w-; 021 is ----w---x. The mask drops its set bits from the...