Count Paths with Obstacles

Grid / Path ★★☆☆

Count distinct top-left to bottom-right paths through a 7×7 warehouse grid with walls (right or down moves only).

A1:G7 is a 7×7 warehouse layout. 0 is open floor, 1 is a shelf you can’t walk through. A picker enters at A1 (top-left) and must reach G7 (bottom-right), moving only right or down at each step.

Output the number of distinct routes through the open cells.

Without walls this would be C(12, 6) = 924 routes. The walls slash that dramatically — the formula has to enumerate and filter, which is why the recursive + over branches works cleanly here.

Input

Range A1:G7

	B	C	D	E	F
1	0	0	0	0	0
2	0	1	0	0	0
3	0	0	0	1	0
4	1	0	0	0	1
5	0	0	1	0	0
6	0	0	0	0	1
7	0	0	0	0	0

Your output

Hint

Branching recursion. Three base cases: out-of-bounds returns 0, hitting a wall returns 0, reaching the goal returns 1. Otherwise recurse down + right and SUM the results.

Solution

=LET(
  tbl, A1:G7,
  ros, ROWS(tbl),
  cols, COLUMNS(tbl),
  fx, LAMBDA(me, ro, co,
    IF(OR(ro>ros, co>cols), 0,
    IF(INDEX(tbl, ro, co)=1, 0,
    IF(AND(ro=ros, co=cols), 1,
      me(me, ro+1, co) + me(me, ro, co+1)
    )))
  ),
  fx(fx, 1, 1)
)