Calculate the number of ways of getting to the pizza without stepping on bombs (you can move up and right)
My solution was to calculate the number of ways of getting from the snail to the pizza (without the including the bombs) and subtracting from that number the number of ways of getting from any bomb to the pizza. Thereafter, adding to it the number of ways where you step on two bombs and get to the pizza. Finally, I add to that number the number of ways of stepping on three bombs and getting to the pizza. (All from the Inclusion–exclusion principle). My final answer was: $$31293$$ Am I correct? Can you spot any mistakes I've made along the way? Thank you!
(Edit: I counted those ways by looking at the permutations of choosing a certain number of steps to the right, $x$ from the sum of steps to left and right $x+y$, so: $$\binom{x+y}{x}=\binom{x+y}{y}$$ See: How can I find the number of the shortest paths between two points on a 2D lattice grid?)
Simple counting seems less tedious than using the inclusion-exclusion principle:
Every rectangle has a number which denotes the number of ways to reach to that rectangle from the lower-left corner. To reach that number, just add the values of left and down rectangles. Obviously, putting $0$ in place of the bombs before calculations is fitting with that general rule.