Server 1 |
Server 2 |
Server 3 |
Server 4 |
Server 5 |
Server 6 |
Server 7 |
Server 8 |
Server 9 |
Server 10 |
${\color{Red} W}{\color{Red} S{\color{Red} 1}}$ |
${\color{Grey}W }{\color{Grey} S}{\color{Grey} 2}$ |
${\color{Yellow} W}{\color{Yellow} S{\color{Yellow} 3}}$ |
${\color{Brown} W}{\color{Brown} S{\color{Brown} 4}}$ |
${\color{Cyan} W}{\color{Cyan} S{\color{Cyan} 5}}$ |
${\color{Teal}W }{\color{Teal}S }{\color{Teal}6 }$ |
${\color{DarkOrange}W }{\color{DarkOrange} S}{\color{DarkOrange} 7}$ |
${\color{Golden} W}{\color{Golden}S }{\color{Golden} 8}$ |
${\color{Orchid} W}{\color{Orchid}S }{\color{Orchid} 9}$ |
${\color{Emerald} W}{\color{Emerald} S}{\color{Emerald} 1}{\color{Emerald} 0}$ |
${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ |
${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ |
${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ |
${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ |
${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ |
${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ |
${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ |
${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ |
${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ |
${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ |
${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ |
${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ |
${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ |
${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ |
${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ |
${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ |
${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ |
${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ |
${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ |
${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ |
${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 3}$ |
${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 3}$ |
${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 3}$ |
${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 3}$ |
${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 3}$ |
${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 3}$ |
${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 3}$ |
${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 2}$ |
${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 2}$ |
${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 2}$ |
${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ |
${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ |
${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ |
${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ |
${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ |
${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ |
${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ |
${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ |
${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ |
${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ |
${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ |
${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ |
${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ |
${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ |
${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ |
${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ |
${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ |
${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ |
${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ |
${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ |
SOLUTION :-
$\rightarrow$ We have $15$ work stations and $10$ servers.
$\rightarrow$ Select $10$ WorkStations ( $WS$ ) and then connect them with $1$ server each like ${\color{Red} W}{\color{Red} S{\color{Red} 1}}$ to Server1 $, ${\color{Grey}W }{\color{Grey} S}{\color{Grey} 2}$ to Server 2$, ${\color{Yellow} W}{\color{Yellow} S{\color{Yellow} 3}}$ to Server 3 and so on.
$\rightarrow$ So total Workstations ( WS ) selected till now $= 10$ and in each server we have $1$ Workstation connected and is active.
For each server, only one direct connection to that server can be active at any time.
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We want to guarantee that at any time any set of 10 or fewer workstations can simultaneously access different servers via direct connections.
$\rightarrow$ This means that we should always try that 10 workstations are active and running. However if say 7 workstation are not active i.e. only 8 work station are running then that that is not our fault because we have only 15 work sations available.
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Now suppose ${\color{Red} W}{\color{Red} S{\color{Red} 1}}$ which is connected to server 1 that connection is not active
$\rightarrow$ This means that only 9 work stations are active and are accessing the servers.
$\rightarrow$ so in place of ${\color{Red} W}{\color{Red} S{\color{Red} 1}}$'s connection we could activate connection of ${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ or ${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ or ${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 3}$ or ${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ or ${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ .
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$\rightarrow$ SImilarly we can repeat the above step for workstations ${\color{Grey}W }{\color{Grey} S}{\color{Grey} 2}$, ${\color{Yellow} W}{\color{Yellow} S{\color{Yellow} 3}}$ , ${\color{Brown} W}{\color{Brown} S{\color{Brown} 4}}$ , ${\color{Cyan} W}{\color{Cyan} S{\color{Cyan} 5}}$ , ${\color{Teal}W }{\color{Teal}S }{\color{Teal}6 }$ , ${\color{DarkOrange}W }{\color{DarkOrange} S}{\color{DarkOrange} 7}$, ${\color{Golden} W}{\color{Golden}S }{\color{Golden} 8}$, ${\color{Orchid} W}{\color{Orchid}S }{\color{Orchid} 9}$ and ${\color{Emerald} W}{\color{Emerald} S}{\color{Emerald} 1}{\color{Emerald} 0}$ in case they are not active.
$\rightarrow$ For doing this we have to connect each of ${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ or ${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ or ${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 3}$ or ${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ or ${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$ with all the servers.
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$\because$ We need $1$ connection for each of ${\color{Red} W}{\color{Red} S{\color{Red} 1}}$ , ${\color{Grey}W }{\color{Grey} S}{\color{Grey} 2}$, ${\color{Yellow} W}{\color{Yellow} S{\color{Yellow} 3}}$ , ${\color{Brown} W}{\color{Brown} S{\color{Brown} 4}}$ , ${\color{Cyan} W}{\color{Cyan} S{\color{Cyan} 5}}$ , ${\color{Teal}W }{\color{Teal}S }{\color{Teal}6 }$ , ${\color{DarkOrange}W }{\color{DarkOrange} S}{\color{DarkOrange} 7}$, ${\color{Golden} W}{\color{Golden}S }{\color{Golden} 8}$, ${\color{Orchid} W}{\color{Orchid}S }{\color{Orchid} 9}$ and ${\color{Emerald} W}{\color{Emerald} S}{\color{Emerald} 1}{\color{Emerald} 0}$ and $10$ connections for each of ${\color{Green} W}{\color{Green} S}{\color{Green} 1}{\color{Green} 1}$ or ${\color{Blue}W}{\color{Blue}S}{\color{Blue} 1}{\color{Blue} 2}$ or ${\color{Magenta} W}{\color{Magenta} S}{\color{Magenta} 1}{\color{Magenta} 3}$ or ${\color{Purple} W}{\color{Purple}S }{\color{Purple}1 }{\color{Purple} 4}$ or ${\color{Orange}W }{\color{Orange}S}{\color{Orange} 1}{\color{Orange}5 }$
$\therefore$ Total connections required $= 10 + (5*10) = 60.$