Toads and frogs game

Therefore, the number of moves needed to solve the problem is. These may be short and not well grounded, but can be varified by experimenting with the applet. The bottom line is that the right moves are actually forced: at every given moment excluding the starting configuration there is only one right move.

Whichever jump you choose, you are stuck on the next move. Unless, of course, the "hole" moves to an end square. In which case you get stuck on the second move. To solve the puzzle is to move all frogs to the right and all toads to the left. When this is done, we can think of the result as having a new puzzle where backward-looking frogs became toads, and the backward-looking toads turned into forward-looking frogs.

A sequence of moves that solved the original puzzle will solve the new puzzle if read backwards. For every M and N, there are two solutions. One starts with a leftward slide, the other with a rightward slide.

For this I do not have an explanation yet. In the picture, we see at the most left level the first two possible moves. With red forecolor are signed moves that were taken. With black backcolor are signed moves that were taken but cancelled because they didn't lead to the goal. After the first move, "L from 2 to 3" we see, that moves "L from 1 to 2" and "L from 0 to 1" don't lead to the end of the game. So we take the alternative second move, "R from 4 to 2". In the third step, we explore the possible move "L from 3 to 4".

Since this is not a winning one, we have to take the move "R from 5 to 4". We continue this procedure until we reach the goal. We also have to think that the game can't be solved. For the solution, I've programmed a method called TryThis. It is a recursive method, so it is using an edge condition and a recursive call. The edge condition is reached when there are no more elements left in the array of all possible moves.

The method TryThis takes one parameter which describes the number of the step or the depth of the tree - for example "L 1 2" and "R 4 2" have the same step number. In the method TryThis , we call the method FindAll. With this method, we find all possible moves in a "situation" and we return the moves in an ArrayList. I've tried to present the solution in three different ways. First I've used a ListBox to view, if my solution works.

Can you predict how many moves it will take you? Can you swap the frogs over when the number of red and blue frogs is not the same? You can use the interactive environment below or explore with counters.

Full Screen and tablet version Can you see any patterns in the sequence of moves that it takes to swap the frogs over? Can you explain why those patterns occur?

Can you describe a method for swapping all the frogs over in the minimum number of moves? Main menu Search. Build Two: Food Flies Divide the playing area into the three areas mentioned in the game rules above: the burrow, the river and the river bank. Build Three: Lily Pads Now place a variety of lily pads on the river. Grade Level Outcomes S1. E1 Hopping, galloping, running, sliding, skipping, leaping S1.

E7 Balance. Discussion Questions What are the critical elements of mature hopping? What are the critical elements of mature jumping for distance? What are different balances we know that can be performed on a poly spot? What are different exercises we know that can be performed on a poly spot?

What are different stretches we know that can be performed on a poly spot? Safety Information Fish should use soft tags when tagging fleeing players consider using foamies a.