$11$

$1$

$11$

$11$

$($a$)111$

$($b$)111$

$($c$)1111$

$($d$)111$

$111$

$|1111$

IIII

IIII

$|1111$

$|11111|$

$|$II$|$

IIIII

$3.$ Suppose that no more than i sticks can be removed at a time from the ith pile $($piles are numbered from top to bottom$).$ Repeat Exercise $1$ with this additional condition.

$a,b$ only