Six magicians A, B, C, D, E, F live in an island. Every Monday, the elders of the island rank the six magicians on their performance during the previous six days.

The rankings published on the previous Monday listed A 1st, B 2nd, C 3rd, D 4th, E 5th and F 6th.

This Monday’s ranking has each magician ranked in a different position than that of the previous Monday. We know that:

1. B’s change in ranking is greatest among the six magicians.

2. The product of D’s rankings for the two weeks is the same as the product of F’s rankings for the two weeks.

Determine the new rankings.

The new rankings are: E is first, D second, F third, A fourth, C fifth, B sixth. 
Start with D and F.  If D is 1, 3, or 5, F is a fractional number.  If D is 6, F is off the chart.  If D is 4, it violates condition #1.  So D must be second, and therefore F must be third.  F has moved three places, so B must move four places (condition #1) to become #6.  That leaves first, fourth and fifth place.  A must move to 4 or 5.  But if A were fifth, it would be a move of four places, violating condition #1.  Therefore A is fourth, leaving first and fifth places.  E can't be five (each has a different ranking), so must be first, leaving C to fifth place.

Posted by Marlene on 2007-05-13 04:07:37