Problem about removal pears from the bucket

pears_in_bucket.c

#include <stdio.h>
#include <stdlib.h>

/**
 * There 16 pears in the bucket 4x4. How to remove 6 pears to guarantee
 * even numbers of pears in each row and column.
 */
int b[16];

int f() {
  int a;
  if (b[0] + b[1] + b[ 2] + b[ 3] + b[ 4] + b[ 5] + b[ 6] + b[ 7] +
      b[8] + b[9] + b[10] + b[11] + b[12] + b[13] + b[14] + b[15] != 10)
    return 0;
  if ((b[ 0] + b[ 1] + b[ 2] + b[ 3]) & 1) return 0;
  if ((b[ 4] + b[ 5] + b[ 6] + b[ 7]) & 1) return 0;
  if ((b[ 8] + b[ 9] + b[10] + b[11]) & 1) return 0;
  if ((b[12] + b[13] + b[14] + b[15]) & 1) return 0;
  if ((b[ 0] + b[ 4] + b[ 8] + b[12]) & 1) return 0;
  if ((b[ 1] + b[ 5] + b[ 9] + b[13]) & 1) return 0;
  if ((b[ 2] + b[ 6] + b[10] + b[14]) & 1) return 0;
  if ((b[ 3] + b[ 7] + b[11] + b[15]) & 1) return 0;
  return 1;
}

int main() {
  int i;
  int c = 0;
  for (i = 0; i < (1 << 16); ++i) {
    int j;
    for (j = 0; j < 16; ++j) b[j] = (i & (1 << j)) ? 1 : 0;
    if (!f()) continue;
    printf("#%d:\n", ++c);
    for (j = 0; j < 16; ++j) {
      printf("%d ", b[j]);
      if ((j & 0x03) == 0x03) printf("\n");
    }
  }
  return 0;
}