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Another, more adventurous flea lives on Z2 (the set of points in the plane with integer coordinates). Initially, the flea is at the origin, i.e., at the point (0,0). In one step, the flea can jump to an adjacent point to the right, to the left, up, or down. In how many ways can this flea perform 100 jumps and end up back at the origin?

Another, more adventurous flea lives on Z2 (the set of points in the plane with integer coordinates). Initially, the flea is at the origin, i.e., at the point (0,0). In one step, the flea can jump to an adjacent point to the right, to the left, up, or down. In how many ways can this flea perform 100 jumps and end up back at the origin?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Another, more adventurous flea lives on Z2 (the set of points in the plane with integer coordinates). Initially, the flea is at the origin, i.e., at the point (0,0). In one step, the flea can jump to an adjacent point to the right, to the left, up, or down. In how many ways can this flea perform 100 jumps and end up back at the origin?
Transcribed Image Text:Another, more adventurous flea lives on Z2 (the set of points in the plane with integer coordinates). Initially, the flea is at the origin, i.e., at the point (0,0). In one step, the flea can jump to an adjacent point to the right, to the left, up, or down. In how many ways can this flea perform 100 jumps and end up back at the origin?
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