Concept:
To find the day of a later date, count the number of days between the two dates and divide by \(7\).
The remainder gives the day shift.
Step 1: Count days from \(15^{th}\) August to \(2^{nd}\) October.
From \(15^{th}\) August to \(31^{st}\) August:
\[
16\text{ days}
\]
September has:
\[
30\text{ days}
\]
From \(1^{st}\) October to \(2^{nd}\) October:
\[
2\text{ days}
\]
Total difference:
\[
16+30+2=48
\]
Step 2: Find odd days.
\[
48\div 7=6\text{ remainder }6
\]
So the day shifts by \(6\) days.
Step 3: Count from Wednesday.
Starting from Wednesday:
\[
1\rightarrow Thursday
\]
\[
2\rightarrow Friday
\]
\[
3\rightarrow Saturday
\]
\[
4\rightarrow Sunday
\]
\[
5\rightarrow Monday
\]
\[
6\rightarrow Tuesday
\]
Step 4: Final answer.
\[
\boxed{\text{Tuesday}}
\]
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