Unity入門的なノリで書いた。

TouchTheNumber.cs

using UnityEngine;
using System.Collections;

struct Panel
{
    public Rect rect;
    public bool pushed;
    public int num;    
}

public class TouchTheNumber : MonoBehaviour
{
    private int nextNum = 0;
    private Panel[,] panels;

    // Use this for initialization
    void Start ()
    {
        int len = 5;
        int panelSize = Screen.width / len;

        panels = new Panel[len, len];

        int len_x = panels.GetLength (0);
        int len_y = panels.GetLength (1);        
        for (int i  = 0; i< len_x; i++) {
            for (int j = 0; j< len_y; j++) {
                panels [i, j].rect = new Rect (j * panelSize, i * panelSize, panelSize, panelSize);
                panels [i, j].pushed = false;
                panels [i, j].num = i * len_y + j;
            }
        }
        buttonShuffle ();
    }
    
    void initPanels ()
    {
        int len_x = panels.GetLength (0);
        int len_y = panels.GetLength (1);        

        for (int i  = 0; i< len_x; i++) {
            for (int j = 0; j < len_y; j++) {
                panels [i, j].pushed = false;
            }
        }
    }
    
    void buttonShuffle ()
    {
        int len_x = panels.GetLength (0);
        int len_y = panels.GetLength (1);        

        // shuffle!
        for (int i = 0; i < len_x*len_y; i++) {
            int random = Random.Range (0, len_x * len_y - i);
            int x = random / len_x;
            int y = random % len_y;
            int tmp = panels [x, y].num;
            
            int tmp2 = len_x * len_y - 1 - i;
            int xx = tmp2 / len_x;
            int yy = tmp2 % len_y;
            panels [x, y].num = panels [xx, yy].num;
            panels [xx, yy].num = tmp;
        }
    }

    void OnGUI ()
    {
        int len_x = panels.GetLength (0);
        int len_y = panels.GetLength (1);        

        for (int i  = 0; i< len_x; i++) {
            for (int j = 0; j< len_y; j++) {
                if (!panels [i, j].pushed && GUI.Button (panels [i, j].rect, panels [i, j].num.ToString ())) {
                    if (panels [i, j].num == nextNum) {                        
                        panels [i, j].pushed = true;
                        nextNum++;
                    }
                }
            }
        }

        if (nextNum >= len_x * len_y) {
            nextNum = 0;
            initPanels ();
            buttonShuffle ();
        }
    }

    void Update ()
    {
    
    }
}