The question states that the number of students with at least
questions wrong is
. Hence the number that actually get exactly
wrong,
, must be the number that get at least
wrong minus those that get at least
)
wrong. So we have
.
So if we let
be the total number of wrongly answered questions then
,
)
,
,
 4^{n-(k+1)} + <br />
\sum_{k=1}^{n-1} 4^{n-(k+1)})
,
} )
(letting
),
,
} )
,
} )
,
(letting
)
),
)
.
(I know I could have explicitly written out the sum, 'spot the pattern' - as I did on paper, but decided this was typographically easier than using an array).
So we have that
)
and solving gives us that
![\color[rgb]{0,0,1} \boxed{n = 5}](http://latex.codecogs.com/png.latex?\color[rgb]{0,0,1} \boxed{n = 5})
.
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About LinkBacksquestions. In the test,
students gave wrong answers to at least
. If the total number of wrong answers is 341, then find the value of n.
