Problem

Who Wants the Money, a game show, distributes prizes that are powers of 2. What is the min...

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?

Step-by-Step Solution

Solution 1

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 .

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