Go: package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

var scanner = bufio.NewScanner(os.Stdin)
var (
	table, ans = [12][12]int{}, [12][12]int{}
)

func main() {
	scanner.Scan()
	n, _ := strconv.Atoi(scanner.Text())
	for i := 0; i < n; i++ {
		for j := 1; j < 11; j++ {
			scanner.Scan()
			input := strings.Split(scanner.Text(), " ")
			tmp := [10]int{}
			for k := range input {
				tmp[k], _ = strconv.Atoi(input[k])
			}
			for l := 1; l < 11; l++ {
				table[j][l] = tmp[l-1]
			}
		}
		check(table, 1, ans)
	}
}

func check(table [12][12]int, i int, ans [12][12]int) {
	if i == 11 {
		solve(table, 2, 1, ans)
		return
	}
	ans[1][i] = 0
	check(table, i+1, ans)
	ans[1][i] = 1
	attack(table, 1, i)
	check(table, i+1, ans)
	attack(table, 1, i)
}

func solve(table [12][12]int, i, j int, ans [12][12]int) {
	if i == 11 {
		flag := true
		for k := 1; k < 11; k++ {
			if table[10][k] == 1 {
				flag = false
				break
			}
		}
		if flag {
			printans(ans)
		}
		return
	}
	if table[i-1][j] == 1 {
		ans[i][j] = 1
		attack(table, i, j)
		if j == 10 {
			solve(table, i+1, 1, ans)
		} else {
			solve(table, i, j+1, ans)
		}
		attack(table, i, j)
		ans[i][j] = 0
	} else {
		ans[i][j] = 0
		if j == 10 {
			solve(table, i+1, 1, ans)
		} else {
			solve(table, i, j+1, ans)
		}
	}
}

func printans(ans [12][12]int) {
	for i := 1; i < 11; i++ {
		for j := 1; j < 11; j++ {
			fmt.Print(ans[i][j])
			if j < 10 {
				fmt.Print(" ")
			}
		}
		fmt.Println()
	}
}

func attack(table [12][12]int, i, j int) {
	table[i][j] = 1 - table[i][j]
	table[i-1][j] = 1 - table[i-1][j]
	table[i+1][j] = 1 - table[i+1][j]
	table[i][j-1] = 1 - table[i][j-1]
	table[i][j+1] = 1 - table[i][j+1]
}

C++: #include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <complex>
#include <cstring>
#include <cstdlib>
#include <string>
#include <cmath>
#include <queue>
using namespace std;

#define REP(i,n) for(int i=0;i<(int)n;++i)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)
#define ALL(c) (c).begin(), (c).end()
const int INF = 1<<30;

bool ans[10][10];
bool ba[10][10];
int dx[] = {-1,0,0,0,1};
int dy[] = {0, -1,0, 1, 0};

bool judge(int x, int y) {
  int res = ba[x][y];
  REP(k,5) {
    int xx = x + dx[k];
    int yy = y + dy[k];
    if (xx < 0 || xx >= 10 || yy < 0 || yy >= 10) continue;
    if (ans[xx][yy]) res++;
  }
  return res % 2;
}

int main() {
  int n;
  cin >> n;
  while(n--) {
    REP(y,10)
      REP(x,10)
      cin >> ba[x][y];
    
    for (int i=0; i<(1<<10); ++i) {
      memset(ans, 0, sizeof(ans));
      REP(j,10)
        if ((i>>j)&1)
          ans[j][0] = 1;
      for(int y=1; y<10; ++y) {
        REP(x,10) {
          if (judge(x,y-1))
            ans[x][y] = 1;
        }
      }
      bool f = 1;
      REP(i,10)
        if (judge(i, 9)) f = 0;
      if (f) 
        break;
    }
    REP(y,10) {
      REP(x,10) {
        if (x) cout << " ";
        cout << ans[x][y];
      }
      cout << endl;
    }
  }
}

C++: 
#include <iostream>
#include <cstring>
#include <cmath>
using namespace std;

int board[12][12];
int used[12][12];

bool lastCheck(){
	for(int y=0;y<10;y++){
		for(int x=0;x<10;x++){
			if(board[y][x])return false;
		}
	}
	return true;
}

bool canPut(int y, int x){
	int sy = y - 1;
	int ty = y + 1;
	int sx = x - 1;
	int tx = x + 1;
	if(sy < 0 || ty >= 10 || sx < 0 || tx >= 10)return false;
	return true;
}

bool allow(int n){
	for(int i=0;i<n;i++){
		int y = i / 10;
		int x = i % 10;

		if(board[y][x] == 0)continue;

		bool ok = false;
		for(int j=n;j<100;j++){
			int ny = j / 10;
			int nx = j % 10;

			int dy = abs(ny - y);
			int dx = abs(nx - x);

			if(dy >= 2)break;
			if(dy + dx <= 1 && canPut(ny, nx)){
				ok = true;
				break;
			}
		}

		if(!ok)return false;
	}
	return true;
}

int pattern[] = {
    0,1,0,
    1,1,1,
    0,1,0
};

void flip(int y, int x){
	int sy = y - 1;
	int sx = x - 1;
	for(int i=0;i<3;i++)for(int j=0;j<3;j++){
		int ny = sy + i;
		int nx = sx + j;
		if(pattern[i*3+j]){
			board[ny][nx] ^= 1;
		}
	}
}

bool dfs(int n){
	if(n >= 10 * 10){
		return lastCheck();
	}
	if(!allow(n)){
		return false;
	}
	int y = n / 10;
	int x = n % 10;

	if(!canPut(y, x)){
		return dfs(n + 1);
	}

	if(dfs(n + 1)){
		return true;
	}

	flip(y, x);
	used[y][x] = 1;

	if(dfs(n + 1))return true;
	
	used[y][x] = 0;
	flip(y, x);

	return false;
}

void solve(){
	memset(used, 0, sizeof(used));
	dfs(0);
}
int main()
{
	int n;
	cin >> n;

	for(int t=0;t<n;t++){
		if(t > 0)cout << endl;
		for(int y=0;y<10;y++){
			for(int x=0;x<10;x++)cin >> board[y][x];
		}
		solve();
		for(int y=0;y<10;y++){
			if(y > 0)cout << endl;
			for(int x=0;x<10;x++){
				if(x > 0)cout << " ";
				cout << used[y][x];
			}
		}
	}
	return 0;
}

C++: 
#include <iostream>
#include <cstring>
#include <cmath>
using namespace std;

int board[12][12];
int used[12][12];

bool lastCheck(){
	for(int y=0;y<10;y++){
		for(int x=0;x<10;x++){
			if(board[y][x])return false;
		}
	}
	return true;
}

bool allow(int n){
	for(int i=0;i<n;i++){
		int y = i / 10;
		int x = i % 10;

		if(board[y][x] == 0)continue;

		bool ok = false;
		for(int j=n;j<100;j++){
			int ny = j / 10;
			int nx = j % 10;

			int dy = abs(ny - y);
			int dx = abs(nx - x);

			if(dy >= 2)break;
			if(dy + dx <= 1){
				ok = true;
				break;
			}
		}

		if(!ok)return false;
	}
	return true;
}

int pattern[] = {
    0,1,0,
    1,1,1,
    0,1,0
};

void flip(int y, int x){
	int sy = y - 1;
	int sx = x - 1;
	for(int i=0;i<3;i++)for(int j=0;j<3;j++){
		int ny = sy + i;
		int nx = sx + j;
		if(ny < 0 || ny >= 10 || nx < 0 || nx >= 10)continue;

		if(pattern[i*3+j]){
			board[ny][nx] ^= 1;
		}
	}
}

bool dfs(int n){
	if(n >= 10 * 10){
		return lastCheck();
	}
	if(!allow(n)){
		return false;
	}
	int y = n / 10;
	int x = n % 10;

	if(dfs(n + 1)){
		return true;
	}

	flip(y, x);
	used[y][x] = 1;

	if(dfs(n + 1))return true;
	
	used[y][x] = 0;
	flip(y, x);

	return false;
}

void solve(){
	memset(used, 0, sizeof(used));
	if(!dfs(0)){
		while(1);
	}
}
int main()
{
	int n;
	cin >> n;

	for(int t=0;t<n;t++){
		for(int y=0;y<10;y++){
			for(int x=0;x<10;x++)cin >> board[y][x];
		}
		solve();
		for(int y=0;y<10;y++){
			for(int x=0;x<10;x++){
				if(x > 0)cout << " ";
				cout << used[y][x];
			}
			cout << endl;
		}
	}
	return 0;
}

C++: #include <iostream>
#include <stdio.h>
#include <utility>
#include <vector>
#include <algorithm>
#include <string>
using namespace std;
int dx[]={-1,0,0,1};
int dy[]={0,0,-1,0};
int main()
{
    int n;
	cin>>n;
	bool fir=true;
	while(n--){
		//if(!fir)cout<<endl;
		int panel[10]={};
		for(int i=0;i<10;i++){
			for(int j=0;j<10;j++){
				int tmp;
				cin>>tmp;
				panel[i]|=tmp<<j;
			}
		}
		for(int i=0;i<(1<<10);i++){//1??????ans?????????
			int ans[10]={};
			ans[0]=i;
			for(int j=0;j<9;j++){//????????????ans????¨????
				for(int k=0;k<10;k++){//?????????????????°???
					int tmp=0;
					for(int l=0;l<4;l++){
						int nx=k+dx[l],ny=j+dy[l];
						if(0<=nx&&nx<10&&0<=ny&&ny<9)tmp+=(ans[ny]>>nx)&1;
					}
					if((tmp+2-(panel[j]>>k)&1)%2)ans[j+1]|=1<<k;
				}
			}
			int check[10];
			for(int j=0;j<10;j++)check[j]=(panel[9]>>j)&1;
			for(int j=0;j<10;j++){
				check[j]+=(ans[8]>>j);
				if((ans[9]>>j)&1){
					for(int k=-1;k<=1;k++){
						int x=j+k;
						if(0<=x&&x<10)check[x]++;
					}
				}
			}
			for(int j=0;j<10;j++)check[j]=check[j]%2;
			if(check[9]==0){
				for(int y=0;y<10;y++){
					for(int x=0;x<10;x++){
						int tmp=(ans[y]>>x)&1;
						printf(x==9?"%d\n":"%d ",tmp);
					}
				}		
				break;
			}
		}
		fir=false;
	}
    return 0;
}