1. Write a function to count the number of distinct bit patterns that can be formed with a given number of bits.
2. Create a program to find the maximum XOR of any two numbers in an array.
3. Write a function to determine if a number is a power of two using bit manipulation.
4. Implement a function to swap two numbers without using a temporary variable, utilizing bitwise operations.
5. Create a program to find the smallest number that can be formed by rearranging the bits of a number.
6. Write a function to find the two non-repeating elements in an array where every other element appears twice.
7. Create a program to generate all possible subsets of a given set using bit manipulation.
8. Write a function to determine the longest consecutive sequence of 1s in the binary representation of a number.
9. Create a program to find the first missing positive integer using bit manipulation.
10. Write a function to determine if a number is an integer when its square root is computed.
11. Create a program to find the number of set bits in the binary representation of a number using the Kernighan's algorithm.
12. Write a function to check if two numbers have opposite signs using bit manipulation.
13. Create a program to count the number of integers that can be formed by flipping exactly one bit of a given integer.
14. Write a function to find the nth power of two without using multiplication or division.
15. Create a program to find the maximum number of trailing zeros in the binary representation of a number.
16. Write a function to determine if a number can be expressed as the sum of two squares using bit manipulation.
17. Create a program to calculate the number of bit flips required to convert one integer into another.
18. Write a function to find the bitwise AND of all numbers in a given range.
19. Create a program to check if a number is a valid binary representation of a string.
20. Write a function to count how many integers in a range can be expressed as the sum of two distinct primes.
21. Create a program to find the smallest integer greater than a given number that has a specific number of set bits.
22. Write a function to check if a number can be expressed as the product of two distinct primes.
23. Create a program to find the maximum number of distinct integers in an array after performing at most k bit flips.
24. Write a function to determine if a number is a valid base-64 string using bit manipulation.
25. Create a program to find the position of the least significant bit set in a number.
26. Write a function to find the number of integers in a list that can be represented as the sum of two distinct odd primes.
27. Create a program to count how many integers in a range can be represented as the product of three distinct primes.
28. Write a function to find the smallest integer that can be formed by rearranging the bits of a number.
29. Create a program to check if a number can be expressed as the sum of two distinct odd numbers.
30. Write a function to calculate the bitwise XOR of two binary strings.
31. Create a program to determine if a number can be expressed as the sum of three distinct cubes.
32. Write a function to find the index of the first set bit in the binary representation of a number.
33. Create a program to calculate the parity of a number using bit manipulation.
34. Write a function to find the longest sequence of consecutive zeros in the binary representation of a number.
35. Create a program to determine if two numbers can be expressed as the sum of three distinct squares.
36. Write a function to count how many integers in a list can be represented as the sum of three distinct primes.
37. Create a program to calculate the bitwise NOT of a binary string without using the NOT operator.
38. Write a function to check if a number is an ugly number using bit manipulation.
39. Create a program to find the number of integers in a range that can be expressed as the product of two distinct cubes.
40. Write a function to find the smallest integer greater than or equal to a given number that can be expressed as a power of three.