FizzBuzz solved using only bit twiddling. It essentially uses two deterministic finite automata for divisibility testing.
#include <stdio.h>
int f0(unsigned int x) { return x? (x&(1<<31)? f1(x<<1) : f0(x<<1)) : 1; }
int f1(unsigned int x) { return x? (x&(1<<31)? f3(x<<1) : f2(x<<1)) : 0; }
int f2(unsigned int x) { return x? (x&(1<<31)? f0(x<<1) : f4(x<<1)) : 0; }
int f3(unsigned int x) { return x? (x&(1<<31)? f2(x<<1) : f1(x<<1)) : 0; }
int f4(unsigned int x) { return x? (x&(1<<31)? f4(x<<1) : f3(x<<1)) : 0; }
int t0(unsigned int x) { return x? (x&(1<<31)? t1(x<<1) : t0(x<<1)) : 1; }
int t1(unsigned int x) { return x? (x&(1<<31)? t0(x<<1) : t2(x<<1)) : 0; }
int t2(unsigned int x) { return x? (x&(1<<31)? t2(x<<1) : t1(x<<1)) : 0; }
int main(void) {
unsigned int i;
for(i=1; i <= 100; i++) {
if(t0(i)) printf("Fizz");
if(f0(i)) printf("Buzz");
if(!(t0(i)|f0(i))) printf("%u",i);
printf("\n");
}
}