
Step 1: Chinky’s answers b d d c b d a b a b
Step 2: Compare with others Rahul: b d d c b d a b a b ✔️ (exact match)
Sastry (final key): b d d c b d a c a b Only Q8 differs ⇒ So if Chinky had two jigris (Sastry and Rahul), for Q8:
Sastry has 'c', Rahul has 'b' ⇒ not identical ⇒ Chinky leaves it blank
But Chinky wrote 'b' ⇒ copied from Rahul So consistent.
Hence, jigris are Sastry and Rahul.





For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: