= Solution
Use the weekday number as an <array index>. Before adding dates, add one empty entry to each weekday before `start`; otherwise the first date in those columns would appear a week too early. For day $d$, the slot number is $\texttt{start}+d-1$, whose remainder modulo 7 selects the column. The source's example makes clear that `start` counts empty weekday cells, rather than individual printed space characters.<Object Oriented Programming examination paper of the University of Oxford (2015)>[p. 3, Question 1(e) and Figure 1, month(1,30)]{ref}
With `import java.util.*;`, the remaining <Java> code is:
``
final class Column extends ArrayList<Data> {
private static final long serialVersionUID = 1L;
}
static String month(int start, int numDays) {
if (start < 0 || start >= 7 || numDays < 1 || numDays > 31)
throw new IllegalArgumentException("invalid month parameters");
String[] days = {"Su", "Mo", "Tu", "We", "Th", "Fr", "Sa"};
int ncols = days.length;
List<Column> output = new ArrayList<Column>(ncols);
for (int c = 0; c < ncols; ++c) {
Column column = new Column();
column.add(new StringData(days[c], true));
output.add(column);
}
for (int c = 0; c < start; ++c)
output.get(c).add(new StringData("", true));
for (int d = 1; d <= numDays; ++d) {
int c = (start + d - 1) % ncols;
output.get(c).add(new IntegerData(d, false));
}
return printData(output);
}
``
The two-character headers force every column to width two, and right justification aligns one-digit dates with the units digits of two-digit dates. Date $d$ appears in data row $\lfloor(\texttt{start}+d-1)/7\rfloor$, below the header. For `month(1,30)` the visible result is
``
Su Mo Tu We Th Fr Sa
1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30
``
The last physical line may also carry spaces for its empty trailing cells. Every physical line ends with a newline. In particular,
$$
\boxed{\text{weekday}(d)=(\texttt{start}+d-1)\bmod7.}
$$
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