Who Wants the Money, a game show, distributes prizes that are powers of 2. What is the minimum number of prizes that could be distributed from $900?
Here consider the powers of to distribute the prizes from
.
As the minimum number of prizes we need so take the greater powers of which is nearest to $900.
That is
Now the remaining amount is
Again the powers of which is nearest to
is
So the remaining amount is
Again the powers of which is nearest to
is
So the remaining amount is
Now can be written as
Thus total four prizes are distributed from as powers of
which are
,
,
and
.
Therefore the amount is distributed as 1 prize of
, 1 prize of
,1 prize of
and 1 prize of
.
Hence the answer is .