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(2): solution by Dej Mar)

Ah! The offending line of my program, which allowed the erroneoud total listed for my second "solution" for part (v), is:

 FOR n6 = 1 TO tot - n1 - n2 - n4 - n5

in its allowance for n6, the number of 625% copies to not count n3, the number of 125% copies, and thus be higher than the presumed tot would be.  A couple of preceding lines also have this omission, but this line was the one that led to the printing of a tot that was in fact lower than the actual total.

Posted by Charlie on 2012-07-22 10:45:24