Grades 11-12 Video Solutions 2026-2026_11-12

Video Transcription

Video Summary

Question 4. John wants to walk from S to F. He can only walk along the paths marked and only in the directions indicated by the arrows. He must also avoid the black stones. How many different paths can he take? A, 5, B, 6, C, 7, D, 8, or E, 9. First, let's mark these two circles, A and B. Notice how all paths from S to F must either pass through A or B. Now from S, there are two directions John can take. He can go up, where there is one path to A and one path to B, or he can choose to go down, where there is only one path to A. This leads to a total of two paths from S to A and one path from S to B. Now, from circle A, there are two paths to F. From circle B, there's only one path to F. Now, to get the total number of paths from S to F, we can multiply the number of paths from S to A by the number of paths from A to F and add that to the product of the number of paths from S to B and B to F, giving us five total paths, which is answer choice A.

Keywords

path counting

graph traversal

combinatorics

route enumeration

logic puzzle