A10. A four-digit integer has its digits increasing from left to right. When we reverse the order of the digits, we obtain a four-digit integer whose digits decrease from left to right. A third four-digit integer uses exactly the same digits, but in a different order. The sum of the three integers is 26352 .
What is the value of the smallest of the three integers?
Solution
Let the original integer be ' $p q r s$ ', such that $p 10476, which contradicts the definition of 'srqp'. Therefore, $p=6$.

Therefore, from equation (2), we have $s=9$.
Hence, 'pqrs' $=6789$, 'srqp' $=9876$ and, using equation (1), $X=9687$.
The smallest value of the three integers is 6789 .