4. On the board, the product of the numbers $\overline{\text{IKS}}$ and $\overline{\text{KIS}}$ is written, where the letters correspond to different non-zero decimal digits. The middle digits of this product are I, K, S, and o, written in some order, and the outermost digits are equal to each other and different from the middle ones. What is written on the board?
Answer: $169201=269 \cdot 629$ or $193501=359 \cdot 539$.

Solution. Since the problem does not change when I and K are swapped, we can assume that I $=19$, which is impossible. In the case I $+K=8$, the pair (I, K) is $(2,6)$ or $(3,5)$. Since $269 \cdot 629=169201$ and $359 \cdot 539=193501$, both options are suitable. If I $+K=5$, then $(I, K)=(2,3)$. This case is not suitable, as the number $p$ would be a five-digit number.
2) $C=6$. Since $\amalg=C^{2} \bmod 10$ and $C \neq C$, the digit $C$ is 4. From the table, we find that I $+K+4 \in\{13,15\}$, that is, $I+K \in\{9,11\}$. If $I+K=9$, then $I \cdot K \leqslant 20$, and the second inequality in $(*)$ gives $C \leqslant 3$, which is impossible. Let $I+K=11$. Since I and K are different from C and C, the pair (I, K) can only have the values $(2,9)$ or $(3,8)$. Neither of them is suitable, as $294 \cdot 924=271656$ and $384 \cdot 834=320256$