Suppose that Find

Question

Suppose that  Find

Quizplus · Accepted Answer

The only difference between the two given strings is at the 14th character from the left, which is '9f8f' in both. However, in the required string, it has been replaced by 'fd6889bd28f3'. As each character in hexadecimal notation represents 4 bits, so 4 characters represent a total of 16 bits or 2 bytes. Therefore, the change affects the string by 2 bytes, which is equivalent to 16 bits. Now, each group of 4 bits can either represent 0 to 15 (0x0 to 0xF) in hexadecimal notation. Therefore, there are 16 possibilities for each of the 16 bits. As the changes are completely random, we can assume that each possibility has an equal chance of occurring. Therefore, the total number of possible strings that can be formed by replacing 16 bits is 16^16. However, the length of the given and required strings is 46, and the only change is in 16 bits, therefore, we need to subtract the number of strings that can be formed by changing any other 16 bits. This can be calculated by selecting any 16 bits from the remaining 30 bits, which can be done in 30C16 ways. Therefore, the total number of possible valid strings is 16^16 - 30C16. Simplifying this value gives us 84 as the answer.

Suppose That Find