# Solution 84: Pairs of Lattice Paths with Restrictions

Embed

**Published on Mar 21, 2019**- Let's perform careful casework to formulate a recursive argument: How did the paths look like one step before?

Congratulations to Philip Yao, Gabriel N., Jeremy Weissmann, Kunal Gaurav, Evyatar Baranga, Rishav Gupta, Ruben van Erkelens, Nicola C, attyfarbuckle, and Mac KNÖDEL for successfully solving this week's math challenge question! Philip Yao was the first person to solve the question.

Your support is a heartfelt source of encouragement that propels the channel forward.

Please consider taking a second to subscribe in order to express your valuable support and receive notifications for the latest videos!

Any likes, subscriptions, comments, constructive criticisms, etc., are wholeheartedly appreciated.

For more Weekly Math Challenges:

usclip.net/p/PLpoKXj-PWCbaDXYHES37_zX4O-kCWxguM

Sahil Baori2 months agoCan A and B go back and retrace their paths?

LetsSolveMathProblems2 months agoIn some sense, we are retracing the paths of A and B to establish the recurrence in the video. More precisely, to find the relationship between the number of pairs of A and B of length n and the number of pairs of A and B of length n-1, we are considering what should have happened at the final step of A and B AND how A and B should have looked like immediately before the final step in order to get the desired paths at the end.

Sweety XS2 months ago^{+2}Btw how much educated should we be to answer or understand this solution??

Sweety XS2 months ago^{+1}@Aaron He me too

Aaron He2 months ago^{+3}Probably a decent knowledge of recursive functions, which I don't have lol.

Jeremy Weissmann2 months ago^{+3}I may not have been the first to answer but it was nice to see you cover an approach similar to the one I used in this video!