(A) Ben called ahead by telephone and ordered a length of rope which is in integer feet and inches (that is, lengths like 3 feet and 5 inches NOT lengths like 3 feet and 5.5 inches. Also, lengths like 3 feet and 34 inches are untenable.)

When he picked it up, he found that the clerk had wrongly written the order by interchanging the feet and inches. As a result the rope was only 30% of the length he ordered.

What length did he originally order and what length did he get?

(B) If Ben had got p% of the length he ordered, then for what integer values of p from 1 to 100 inclusive are each of the length of the rope he ordered and the length of the rope he received in integer feet and inches?

   10   for F=0 to 11
   20   for I=0 to 11
   30    Ord=12*F+I:Got=12*I+F
   35    if Ord>0 then
   40    :Pct=100*(Got//Ord)
   50    :if Pct=int(Pct) and Pct<100 then print F;I,Pct
   60   next
   70   next

lists the ways of getting all percentages below 100.

ordered
ft inch  pct
 2  1    56
 4  2    56
 6  3    56
 8  4    56
 9  2    30
 10  5   56
 

Only 30% and 56% are possible, other than the 100% that doesn't involve transposition.

In the particular case of (A), he asked for 9'2" and got 2'9", or only 30% of his order.

For cases where more is received than asked for:

ordered
ft inch  pct
0  1    1200
0  2    1200
0  3    1200
0  4    1200
0  5    1200
0  6    1200
0  7    1200
0  8    1200
0  9    1200
0  10   1200
0  11   1200
1  8    485
1  10   550
3  8    225
4  7    160

Posted by Charlie on 2013-12-06 17:05:59