Solved on Sep 08, 2023

Find the minimum number of prizes that can be distributed from $800\$800, where the prizes are powers of 2.

STEP 1

Assumptions1. The prizes are powers of. . The total amount to be distributed is $800.
3. We need to find the minimum number of prizes that can be distributed.

STEP 2

First, we need to understand that the powers of2 are1,2,4,8,16,32,64,128,256,512,1024, and so on.

STEP 3

We need to find the largest power of2 that is less than or equal to 800.Inthiscase,itis800. In this case, it is 512.

STEP 4

Subtract the largest power of2 from the total amount to find the remaining amount.
Remainingamount=TotalamountLargestpowerof2Remaining\, amount = Total\, amount - Largest\, power\, of\,2

STEP 5

Plug in the values for the total amount and the largest power of2 to calculate the remaining amount.
Remainingamount=$800$512Remaining\, amount = \$800 - \$512

STEP 6

Calculate the remaining amount.
Remainingamount=$800$512=$288Remaining\, amount = \$800 - \$512 = \$288

STEP 7

Now, repeat the process with the remaining amount. Find the largest power of2 that is less than or equal to 288.Inthiscase,itis288. In this case, it is 256.

STEP 8

Subtract the largest power of2 from the remaining amount to find the new remaining amount.
Newremainingamount=RemainingamountLargestpowerof2New\, remaining\, amount = Remaining\, amount - Largest\, power\, of\,2

STEP 9

Plug in the values for the remaining amount and the largest power of2 to calculate the new remaining amount.
Newremainingamount=$288$256New\, remaining\, amount = \$288 - \$256

STEP 10

Calculate the new remaining amount.
Newremainingamount=$288$256=$32New\, remaining\, amount = \$288 - \$256 = \$32

STEP 11

Now, notice that the new remaining amount is a power of. So, we can distribute this as a prize.

STEP 12

Count the number of prizes we have distributed. We have distributed one prize of 512,oneprizeof512, one prize of 256, and one prize of $32. So, the minimum number of prizes that can be distributed is.
The minimum number of prizes that could be distributed from $800 is.

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