Here is a picture of a position in 3 row chomp. My notation (i,j,k) corresponds to the rows in chomp having lengths i+j+k, j+k, k. The following picture corresponds to a chosen point in the plane in the grid that follows.

If i,j or k are large, you may need to change scale:

Move the mouse over a grid square below to display the corresponding chomp position above. A blue dot on the grid indicates a winning position for second player. You can not play the game on this page, it's just to show you what the winning moves are. A yellow dot on a blue circle means this is the winning move you need to make from the given position. If a purple dot with yellow circle appears, this means that is the winning move i,j value, but a smaller k value than the current k shown in the grid.

I put a picture with multiple k sheets here (3x20) and here (3x60), but it is harder to see what is going on than just looking at one value of k at a time. Click on the

(i,j,k) = 0, 0, 0

change scale:

When you use large k, small scale, and click on "superimpose", the pictures will look similar to those in a paper by Friedman and Landsberg. Their results are also described in a science news page on chomp.

Because my Javascript program is relatively slow, I only run it for a maximum of k=300, corresponding to max i =215. You can choose a new value here: max i= and reload the page to run with your prefered max i. This might run very slowly depending on your computer.

If you are using a device with a mouse, move over on the grid will show corresponding chomp position and winning move if possible, which is a shaded subset showing what you should leave.

- The positions which are winning for the second player (P positions) are marked by blue circles.
- The red vertical lines pass through values (i,j,k) which can not be P positions because there is a P position of the form (i,j+l,k-l) for some l, which can be reached from this position. These lines may not all show up properly at small scales with a small browser window.
- The blue digonal lines pass through values (i,j,k) which can not be P positions because there is a P position of the form (i+j+l,0,k-l) which can be reached from this position.
- The gray diagonal lines pass through values (i,j,k) which can not be P positions because there is a P position, marked on the graph by a blue dot, of the form (i+l,j-l,k), which can be reached from this position.

- Starting position is k=0 and a column of blue dots with i=1
- Transfer necessary k-1 and below data to k level:
- put a red mark in the square below where any blue dot is for the k-1 level
- put a red mark in the square below where any red mark is for the k-1 level
- put a blue mark in the square to the immediate left of a blue dot in (i,0,k-1) position
- put a blue mark in the square to the immediate left of a blue mark in (i,0,k-1) position
- Any blue line in the bottom row now is extended diagonally to the left

- Fill in k level:
- Starting from the bottom row and working left to right, fill in a blue dot in the first place where there is no blue, red or gray mark
- When you fill in a blue dot, fill in all the diagonally to the left and above squares with grey lines
- After doing this, go to the next row and repeat
- If you put a blue dot in the first column, then there are no more blue dots to add

- (i-ℓ,j,k)
- (i+ℓ,j-ℓ,k)
- (0,j-ℓ,k)
- (i,j+ℓ,k-ℓ)
- (i+j+ℓ,0,k-ℓ)
- (0,0,k-ℓ)

Playing chomp means taking bites out of the "chocolate bar". On each move you take out a whole numnber of squares, by taking out a square and all squares that are not below or left of it. The bottom left corner is bad, so you lose if you are forced to take that on your move. So moving the sliders above give all possible moves for the above bar, including taking all the bar, which is a loosing move.

- type 1 → type 3 → type 6
- type 2 → type 5

- If it is to the right of a blue dot, then you just move to that blue dot.
- If it's on a grey line, then move to the blue dot on that gray line.
- If it's on a red line, then you have to go to a smaller value of k and find the corresponding position of the form (i,j+l,k-ℓ)
- If it's on a blue line, you have to go to a smaller value of k and find the corresponding position of the form (i+j+l,0,k-ℓ)
- If you are at a position (i,j,k) and there is some position of the form (0,j-ℓ,k), then move to that position.
- Mouse over the positions will display the corresponding values in the diagram.
- There may be more that one winning move, but for simplicty I only show one

- Andries E. Brouwer's page on Chomp includes many results and lots more references
- Doran Zeilberg's page on Chomp, someone who has done a lot of work on Chomp
- Steven Byrnes's paper on poset games, which includes chomp.