In ISO week numbering, Monday is the first day of the week, so that alone narrows it down to one of the odd-numbered modes.
Per Wikipedia:
There are mutually equivalent descriptions of week 01:
- the week with the year’s first Thursday in it (the formal ISO definition),
- the week with 4 January in it,
- the first week with the majority (four or more) of its days in the starting year, and
- the week starting with the Monday in the period 29 December – 4 January.
The third of those descriptions matches “with more than 3 days this year” from the table above, so now we’ve narrowed it down to either 1 or 3.
Finally, still from Wikipedia (emphasis added):
If 1 January is on a Monday, Tuesday, Wednesday or Thursday, it is in week 01. If 1 January is on a Friday, Saturday or Sunday, it is in week 52 or 53 of the previous year (there is no week 00).
Hence, the range must be 1-53, not 0-53. This in turn means the right mode is mode 3.