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Question Number 16936 by Tinkutara last updated on 28/Jun/17
In the diagram, it is possible to travel  only along an edge in the direction  indicated by the arrow. How many  different routes from A to B are there  in all?
$$\mathrm{In}\:\mathrm{the}\:\mathrm{diagram},\:\mathrm{it}\:\mathrm{is}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{travel} \\ $$$$\mathrm{only}\:\mathrm{along}\:\mathrm{an}\:\mathrm{edge}\:\mathrm{in}\:\mathrm{the}\:\mathrm{direction} \\ $$$$\mathrm{indicated}\:\mathrm{by}\:\mathrm{the}\:\mathrm{arrow}.\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{different}\:\mathrm{routes}\:\mathrm{from}\:\mathrm{A}\:\mathrm{to}\:\mathrm{B}\:\mathrm{are}\:\mathrm{there} \\ $$$$\mathrm{in}\:\mathrm{all}? \\ $$
Commented by Tinkutara last updated on 28/Jun/17
Commented by ajfour last updated on 28/Jun/17
N=(1×3)+(2×1×3)+(2×1)     =3+6+2 = 11 .
$$\mathrm{N}=\left(\mathrm{1}×\mathrm{3}\right)+\left(\mathrm{2}×\mathrm{1}×\mathrm{3}\right)+\left(\mathrm{2}×\mathrm{1}\right) \\ $$$$\:\:\:=\mathrm{3}+\mathrm{6}+\mathrm{2}\:=\:\mathrm{11}\:. \\ $$
Commented by Tinkutara last updated on 28/Jun/17
Please explain.
$$\mathrm{Please}\:\mathrm{explain}. \\ $$
Commented by ajfour last updated on 28/Jun/17
(A→Y)×(Y→B)  +(A→X)×(X→B)  +(A→X)×(X→Y)×(Y→B)  =1×3  +  2×1  +  2×1×3  = 11 .
$$\left(\mathrm{A}\rightarrow\mathrm{Y}\right)×\left(\mathrm{Y}\rightarrow\mathrm{B}\right) \\ $$$$+\left(\mathrm{A}\rightarrow\mathrm{X}\right)×\left(\mathrm{X}\rightarrow\mathrm{B}\right) \\ $$$$+\left(\mathrm{A}\rightarrow\mathrm{X}\right)×\left(\mathrm{X}\rightarrow\mathrm{Y}\right)×\left(\mathrm{Y}\rightarrow\mathrm{B}\right) \\ $$$$=\mathrm{1}×\mathrm{3}\:\:+\:\:\mathrm{2}×\mathrm{1}\:\:+\:\:\mathrm{2}×\mathrm{1}×\mathrm{3}\:\:=\:\mathrm{11}\:. \\ $$
Commented by Tinkutara last updated on 29/Jun/17
Thanks Sir!
$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$

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