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 re: solution by Charlie)

Charlie,

The problem text coud be regared as a bit ambiguous in regard to which buttons may be used. One can interpret the specified buttons that are permissible for utilization are limited to each and every one of the operational buttons: 10%, 80%, 125%, 128%, 512%, 625% -- in which case my solution is valid. Yet, I will agree that the note does provide the implication that only the buttons to be used for each case are those that are given to be used at least once - in which case your solution is mostly correct* and confounds the possible reason as to why K Sengupta would intro the problem with mentioning the break down of the 100% button and not mention the unavailability of the other buttons in this preface.

*[Your second solution given for case (v) 4 1 1 1 1 4 is not 11 but 12, thus it is not a valid solution.]

Posted by Dej Mar on 2012-07-22 06:38:51