Solution
Chomp on a Four-by-Seven Bar
Show the problem again
Chomp is played on a rectangular bar of 4 rows and 7 columns of squares. The bottom-left square is poisoned. A move chooses a square and eats it together with every square that is weakly above it and weakly to its right. A player who must eat the poisoned square (because it is the only square left) loses. The first player has exactly one winning opening bite. After that bite, how many squares (including the poisoned one) remain? Answer with an integer.
Worked solution
Number rows from the bottom as 0 to 3 and columns from the left as 0 to 6. The opening bite at row 2, column 3 is the only winning first move: it removes the 2 rows × 4 columns block in the upper right, leaving two full rows of 7 beneath two rows of 3. Remaining squares: 7 + 7 + 3 + 3 = 20. No simple formula is known for general rectangles (strategy stealing proves the first player wins but not how), so one verifies by exhaustive search over the positions, which are just staircase shapes inside the rectangle; the search finds that every other first bite allows the second player to win.
Source: Chomp, introduced by David Gale (1974). Statement written for AxiomIQ.