There should also be a mode of challenge where you set up the starting positions youself, or another player challenging you does it themselves.
Other mode ideas I have:
1. Every x seconds, a bomb explodes, rearranging the order of things to random degrees. Perhaps a difficulty mode could control the extent that it swaps number placement?
2. Arcade Mode: Complete the challenge once and move on to a more arduous setup with more numbers. Perhaps a new row could be added each time one level is passed.
3. Foreign Mode: Play with numbers in a different language. That's all.
Should be the easiest to make at least.
4. Item Mode: Items that recharge which allow you to do certain, useful things, like swap any 2 numbers, turn off the move counter momentarily to increase your score, etc. In mulitplayer mode, you could have an opponent with their own recharging items that can counter the player's actions, and player 1 can do the same as his or her opponent plays the game himself or herself.
5. Memory Mode: Show the player all of the numbers at the start or the game, and when they first move a number, they all flip over so that you can't see them and have to rememebe what numbers were in which locations.