How many different messages can be transmitted in n microseconds using three different signals…
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How many different messages can be transmitted in n microseconds using three different signals if one signal requires 1 microsecond for transmittal, the other two signals require 2 microseconds each for transmittal, and a signal in a message is followed immediately by the next signal?
I initially got it wrong because I put as the initial condition: $a_0=0, space a_1=1$
I found this solution online:
Why is the initial condition $a_2=3$, and not $a_2=2$? It says the other two signals require $2$ microseconds, so I believe $a_2=2$ because in $2$ microseconds we can only send $2$ signals.
sequences-and-series combinatorics discrete-mathematics
asked Apr 21 '14 at 22:43
Al JebrAl Jebr
4,21243276
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add a comment |
$begingroup$
How many different messages can be transmitted in n microseconds using three different signals if one signal requires 1 microsecond for transmittal, the other two signals require 2 microseconds each for transmittal, and a signal in a message is followed immediately by the next signal?
I initially got it wrong because I put as the initial condition: $a_0=0, space a_1=1$
I found this solution online:
Why is the initial condition $a_2=3$, and not $a_2=2$? It says the other two signals require $2$ microseconds, so I believe $a_2=2$ because in $2$ microseconds we can only send $2$ signals.
sequences-and-series combinatorics discrete-mathematics
asked Apr 21 '14 at 22:43
Al JebrAl Jebr
4,21243276
$endgroup$
2
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If "A" takes $1$ microsecond and "B" and "C" take $2$, then in $2$ microseconds you can send any of the following: "AA", "B", or "C".
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– mjqxxxx
Apr 21 '14 at 23:00
2
$begingroup$
You can also start at $0$ by noting there's exactly one message you can send in $0$ microseconds, namely the empty message (no signal). Then the recursion naturally gives you $a_2=a_1+2a_0=1+2cdot 1=3$.
$endgroup$
– celtschk
Apr 21 '14 at 23:09
add a comment |
$begingroup$
How many different messages can be transmitted in n microseconds using three different signals if one signal requires 1 microsecond for transmittal, the other two signals require 2 microseconds each for transmittal, and a signal in a message is followed immediately by the next signal?
I initially got it wrong because I put as the initial condition: $a_0=0, space a_1=1$
I found this solution online:
Why is the initial condition $a_2=3$, and not $a_2=2$? It says the other two signals require $2$ microseconds, so I believe $a_2=2$ because in $2$ microseconds we can only send $2$ signals.
sequences-and-series combinatorics discrete-mathematics
asked Apr 21 '14 at 22:43
Al JebrAl Jebr
4,21243276
$endgroup$
How many different messages can be transmitted in n microseconds using three different signals if one signal requires 1 microsecond for transmittal, the other two signals require 2 microseconds each for transmittal, and a signal in a message is followed immediately by the next signal?
I initially got it wrong because I put as the initial condition: $a_0=0, space a_1=1$
I found this solution online:
Why is the initial condition $a_2=3$, and not $a_2=2$? It says the other two signals require $2$ microseconds, so I believe $a_2=2$ because in $2$ microseconds we can only send $2$ signals.
sequences-and-series combinatorics discrete-mathematics
sequences-and-series combinatorics discrete-mathematics
asked Apr 21 '14 at 22:43
Al JebrAl Jebr
4,21243276
asked Apr 21 '14 at 22:43
Al JebrAl Jebr
4,21243276
edited Dec 6 '18 at 18:10
Al Jebr
asked Apr 21 '14 at 22:43
Al JebrAl Jebr
4,21243276
asked Apr 21 '14 at 22:43
Al JebrAl Jebr
4,21243276
asked Apr 21 '14 at 22:43
Al JebrAl Jebr
4,21243276
4,21243276
2
$begingroup$
If "A" takes $1$ microsecond and "B" and "C" take $2$, then in $2$ microseconds you can send any of the following: "AA", "B", or "C".
$endgroup$
– mjqxxxx
Apr 21 '14 at 23:00
2
$begingroup$
You can also start at $0$ by noting there's exactly one message you can send in $0$ microseconds, namely the empty message (no signal). Then the recursion naturally gives you $a_2=a_1+2a_0=1+2cdot 1=3$.
$endgroup$
– celtschk
Apr 21 '14 at 23:09
add a comment |
2
$begingroup$
If "A" takes $1$ microsecond and "B" and "C" take $2$, then in $2$ microseconds you can send any of the following: "AA", "B", or "C".
$endgroup$
– mjqxxxx
Apr 21 '14 at 23:00
2
$begingroup$
You can also start at $0$ by noting there's exactly one message you can send in $0$ microseconds, namely the empty message (no signal). Then the recursion naturally gives you $a_2=a_1+2a_0=1+2cdot 1=3$.
$endgroup$
– celtschk
Apr 21 '14 at 23:09
2
2
$begingroup$
If "A" takes $1$ microsecond and "B" and "C" take $2$, then in $2$ microseconds you can send any of the following: "AA", "B", or "C".
$endgroup$
– mjqxxxx
Apr 21 '14 at 23:00
$begingroup$
If "A" takes $1$ microsecond and "B" and "C" take $2$, then in $2$ microseconds you can send any of the following: "AA", "B", or "C".
$endgroup$
– mjqxxxx
Apr 21 '14 at 23:00
2
2
$begingroup$
You can also start at $0$ by noting there's exactly one message you can send in $0$ microseconds, namely the empty message (no signal). Then the recursion naturally gives you $a_2=a_1+2a_0=1+2cdot 1=3$.
$endgroup$
– celtschk
Apr 21 '14 at 23:09
$begingroup$
You can also start at $0$ by noting there's exactly one message you can send in $0$ microseconds, namely the empty message (no signal). Then the recursion naturally gives you $a_2=a_1+2a_0=1+2cdot 1=3$.
$endgroup$
– celtschk
Apr 21 '14 at 23:09
add a comment |
2 Answers
2
active
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Promoting a comment from mjqxxxx to a CW answer
If "A" takes 1 microsecond and "B" and "C" take 2, then in 2 microseconds you can send any of the following: "AA", "B", or "C".
$endgroup$
add a comment |
$begingroup$
i found a online solution in which it is showing An = An-1+An-2 because we have two choise here either we can send first signal which 1 second time or we can send another signal which takes two second time anyone of them we can send first so i think the value of A1 = 1 because in 1st second we can send a signal which takes 1 second time and A2 = 1 because in 2 second we cannot send two signal which takes 1 second it is cleared by question so in two second we can send only one signal which takes two second.
answered Mar 12 '18 at 16:19
Yogesh SinghYogesh Singh
1
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$begingroup$
It is possible to post mathematical notation, including subscripts and superscripts, using $LaTeX$ syntax withMathJax. See this short introduction and its links to more detailed information.
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– hardmath
Mar 12 '18 at 17:11
add a comment |
Your Answer
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2 Answers
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2 Answers
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$begingroup$
Promoting a comment from mjqxxxx to a CW answer
If "A" takes 1 microsecond and "B" and "C" take 2, then in 2 microseconds you can send any of the following: "AA", "B", or "C".
$endgroup$
add a comment |
$begingroup$
Promoting a comment from mjqxxxx to a CW answer
If "A" takes 1 microsecond and "B" and "C" take 2, then in 2 microseconds you can send any of the following: "AA", "B", or "C".
$endgroup$
add a comment |
$begingroup$
Promoting a comment from mjqxxxx to a CW answer
If "A" takes 1 microsecond and "B" and "C" take 2, then in 2 microseconds you can send any of the following: "AA", "B", or "C".
$endgroup$
Promoting a comment from mjqxxxx to a CW answer
If "A" takes 1 microsecond and "B" and "C" take 2, then in 2 microseconds you can send any of the following: "AA", "B", or "C".
answered Dec 6 '18 at 4:27
community wiki
Ross Millikan
add a comment |
add a comment |
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i found a online solution in which it is showing An = An-1+An-2 because we have two choise here either we can send first signal which 1 second time or we can send another signal which takes two second time anyone of them we can send first so i think the value of A1 = 1 because in 1st second we can send a signal which takes 1 second time and A2 = 1 because in 2 second we cannot send two signal which takes 1 second it is cleared by question so in two second we can send only one signal which takes two second.
answered Mar 12 '18 at 16:19
Yogesh SinghYogesh Singh
1
$endgroup$
$begingroup$
It is possible to post mathematical notation, including subscripts and superscripts, using $LaTeX$ syntax withMathJax. See this short introduction and its links to more detailed information.
$endgroup$
– hardmath
Mar 12 '18 at 17:11
add a comment |
$begingroup$
i found a online solution in which it is showing An = An-1+An-2 because we have two choise here either we can send first signal which 1 second time or we can send another signal which takes two second time anyone of them we can send first so i think the value of A1 = 1 because in 1st second we can send a signal which takes 1 second time and A2 = 1 because in 2 second we cannot send two signal which takes 1 second it is cleared by question so in two second we can send only one signal which takes two second.
answered Mar 12 '18 at 16:19
Yogesh SinghYogesh Singh
1
$endgroup$
$begingroup$
It is possible to post mathematical notation, including subscripts and superscripts, using $LaTeX$ syntax withMathJax. See this short introduction and its links to more detailed information.
$endgroup$
– hardmath
Mar 12 '18 at 17:11
add a comment |
$begingroup$
i found a online solution in which it is showing An = An-1+An-2 because we have two choise here either we can send first signal which 1 second time or we can send another signal which takes two second time anyone of them we can send first so i think the value of A1 = 1 because in 1st second we can send a signal which takes 1 second time and A2 = 1 because in 2 second we cannot send two signal which takes 1 second it is cleared by question so in two second we can send only one signal which takes two second.
answered Mar 12 '18 at 16:19
Yogesh SinghYogesh Singh
1
$endgroup$
i found a online solution in which it is showing An = An-1+An-2 because we have two choise here either we can send first signal which 1 second time or we can send another signal which takes two second time anyone of them we can send first so i think the value of A1 = 1 because in 1st second we can send a signal which takes 1 second time and A2 = 1 because in 2 second we cannot send two signal which takes 1 second it is cleared by question so in two second we can send only one signal which takes two second.
answered Mar 12 '18 at 16:19
Yogesh SinghYogesh Singh
1
answered Mar 12 '18 at 16:19
Yogesh SinghYogesh Singh
1
answered Mar 12 '18 at 16:19
Yogesh SinghYogesh Singh
1
answered Mar 12 '18 at 16:19
Yogesh SinghYogesh Singh
1
1
$begingroup$
It is possible to post mathematical notation, including subscripts and superscripts, using $LaTeX$ syntax withMathJax. See this short introduction and its links to more detailed information.
$endgroup$
– hardmath
Mar 12 '18 at 17:11
add a comment |
$begingroup$
It is possible to post mathematical notation, including subscripts and superscripts, using $LaTeX$ syntax withMathJax. See this short introduction and its links to more detailed information.
$endgroup$
– hardmath
Mar 12 '18 at 17:11
$begingroup$
It is possible to post mathematical notation, including subscripts and superscripts, using $LaTeX$ syntax with
MathJax. See this short introduction and its links to more detailed information.$endgroup$
– hardmath
Mar 12 '18 at 17:11
$begingroup$
It is possible to post mathematical notation, including subscripts and superscripts, using $LaTeX$ syntax with
MathJax. See this short introduction and its links to more detailed information.$endgroup$
– hardmath
Mar 12 '18 at 17:11
add a comment |
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2
$begingroup$
If "A" takes $1$ microsecond and "B" and "C" take $2$, then in $2$ microseconds you can send any of the following: "AA", "B", or "C".
$endgroup$
– mjqxxxx
Apr 21 '14 at 23:00
2
$begingroup$
You can also start at $0$ by noting there's exactly one message you can send in $0$ microseconds, namely the empty message (no signal). Then the recursion naturally gives you $a_2=a_1+2a_0=1+2cdot 1=3$.
$endgroup$
– celtschk
Apr 21 '14 at 23:09