A copy machine features 7 buttons for making copies, ranging from 10% to 625% in size. The buttons are: 10%, 80%, 100%, 125%, 128%, 512%, 625%.

If the 100% button breaks down, how can you make a 100% copy in a minimum number of steps using:

(i) Each of the buttons 10%, 80% and 625% at least once?

(ii) Each of the buttons 10%, 512% and 625% at least once?

(iii) Each of the buttons 10%, 80%, 512% and 625% at least once?

(iv) Each of the buttons 10%, 80%, 128%, 512% and 625% at least once?

(v) Each of the buttons 10%, 80%, 125%, 128%, 512% and 625% at least once?

Note: In each of the five cases only the specified buttons must be used. Utilization of any button(s) not included in a given case is not permissible.

(In reply to solution by Dej Mar)

The note excludes using any buttons not specified in the particular subsection of the problem being solved.

Posted by Charlie on 2012-07-22 02:34:28