How this calculation works
Count shortest grid paths that never visit one specified grid point.
THE FORMULA
Total monotone paths minus paths passing through the blocked pointA worked example
There are 35 paths to (4,3), of which 18 pass through (2,1).
Good to know
Only right and up steps are allowed.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count shortest grid paths that never visit one specified grid point.
The primary result is labeled “Allowed paths”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Only right and up steps are allowed.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
There are 35 paths to (4,3), of which 18 pass through (2,1).
Which rule does this calculator apply?
Total monotone paths minus paths passing through the blocked point