PATHS
Number Theory
Level
2
YOU WISH TO TRAVEL FROM A TO B , ALONG THE LINES AS SHOWN IN THE SKETCH . YOU MAY ONLY MOVE DOWNWARDS . THE NUMBER OF DIFFERENT PATHS FROM A TO B IS
I KINDLY REQUEST YOU TO TAKE THE IMAGE WITH A IN THE TOP AND B IN THE BOTTOM
The answer is 11.
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1 solution
With the center line, we could have 3 paths when crossing to the center(it's so obvious, though) to the end...on the Y and Z paths (please refer to the image), it gives us only two paths . I named it Y1 and Y2. Y1 enters the center that gives us 3 paths as stated earlier..and Y2 gives only 1 path because of the restriction of the problem. so the possible paths on Y is Y2+ Y1...so it 4. They are they same on Z so that gives us 8 and added with 3 from the center line's path, it's 11. *smiles..