This is the story of Whitey, the polar bear, who lived on ice floes in the arctic.
At first you see Whitey swimming in the arctic waters looking for an ice floe to climb onto.
Click an ice floe with a low number to start the game.
Whitey cannot not stay long on any ice floe because the floes are melting.
At any move, he must jump to another of the ice floes left, the next always carrying a bigger number than the last.
How long can you keep Whitey happy?

Before you start, turn on Smart Moves via View/Options/Board/SmartMoves.
Click a board position to drop a Whitey to mark the starting position.
From now on click numbers with increasing value (like 2,5,7,11,12....)

You can only visit a destination which carries a number bigger than the number of the previous destination.
You can jump as far as you like over unvisited numbers, but they will disappear. (In some variants the jumped numbers stay).
You can also jump over empty positions.
You can go into any of eight directions and you can turn with every move.

Your goal is to visit as many ice floes as possible.
The number of positions you have visited as well as the length of the longest known tour are shown at the right border. The border also shops the number of the ice floe the bear is on.
All solutions have been found by hand, so you might be able to improve on them.

30 fixed setups:
Variant 1 to 5: 16 destinations on 4x4 board.
Variant 6 to 10: 25 destinations on 5x5 board.
Variant 11 to 15: 36 destinations on 6x6 board.
Jumped numbers stay:
Variant 16 to 20: 16 destinations on 4x4 board.
Variant 21 to 25: 25 destinations on 5x5 board.
Variant 26 to 30: 36 destinations on 6x6 board.

There are also six randomized variants:
- 16 destinations on 4x4 board.
- 25 destinations on 5x5 board.
- 36 destinations on 6x6 board.
Jumped numbers stay:
- 16 destinations on 4x4 board.
- 25 destinations on 5x5 board.
- 36 destinations on 6x6 board.

Note that you can click View/EnlargeBoard to see the board better.
Also note that there is an alternative piece set available.

 
Technical Information:
Like my Zillions game 'Flamingos', the game 'Whitey' uses two board positions on the same coordinates in order to display two superimposed images (here number and Whitey with polar bear) at the same time and place.
It might be useful for other authors to study those two games to understand how this has been achieved.
The disadvantage is that during replay the polar bear is not visible.
An alternative method would be to have all images of numbers copied with the polar bear on them, thereby doubling the number of pieces and images.

Related Zillions games: African Tour, Asian Tour, Twisted Tour.