Problem:
Jamal wants to store computer files on floppy disks, each of which has a capacity of megabytes . Three of his files require of memory each, more require each, and the remaining require each. No file can be split between floppy disks. What is the minimal number of floppy disks that will hold all the files?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
First note that the amount of memory needed to store the files is
so the number of disks is at least
However, a disk that contains a -mb file can, in addition, hold only one -mb file, so on each of these disks at least -mb must remain unused. Hence, there is at least of unused memory, which is equivalent to half a disk. Since
at least disks are needed.
To see that disks suffice, note that:
Six disks could be used to store the files containing ;
Three disks could be used to store the three -mb files together with three of the -mb files;
Four disks could be used to store the remaining twelve -mb files.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions