Minus' Solution to

The Painting Crew
Posted June 24 - 30, 1996

Avril is taller than Cary, but shorter than Edwin, tells us that
E > A > C

Denise is taller than Bob, but shorter than Edwin, tells us that
E > B > C.

Bob is shorter than Avril, but taller than Cary, tells us that
A > B > C.

So far we know that Cary is the shortest, that Bob is the second shortest, and that Edwin is the tallest (since none of Bob, Cary, Denise, or Avril are the tallest.)

The last statement, that Denise is taller than three of her crew-mates, indicates that Denise is taller than Cary and Bob (which the previous statements already indicated) and one other person. Since Edwin is known to be the tallest, Denise is taller than Avril.

The order of the crewmates is C < B < A < D < E.

Your Solutions

Oscar Little [oscar@cs.mun.ca] gave Minus the perfect solution. (Note: answer is from tallest to shortest)

Since Erwin is taller than Denise and Denise is taller than the other three, Erwin is tallest and Denise is Second tallest. This leaves Avril who is taller than Bob, who is taller than Cary.

The Answer is Edwin > Denise > Avril > Bob > Cary.

Michael and Bobby Sugar [lsugar@icom.ca] submitted this approach to solving the problem:
Let the participants' names' first letter denote them as A,B,C,D,E and the signs < , > represent shorter or taller in showing relationship.
From the first clue we get: A > C , A < E
From 2nd clue: D > B , D < E , D > A , D > C
from 3rd clue: B < A , B > C
Since C < A, C < B, C < D and C < E (because D < E) thus C is the smallest. Since B < D, B < A , B < E (because D < E) thus B is the 2nd smallest. Since A < D , D < E , A < E thus A is 3rd smallest.
From D < E or 4th clue we conclude that D is 2nd tallest.
By elimination E is the tallest.
Therefore, the required list is Cary, Bob, Avril, Denise, Edwin.

Jim Kearns [jkearns@wiu.k12.pa.us] didn't provide Minus with a full solution, but he knew what he was doing:
(thanks i like it.)

Good work, guys!
Hope you enjoyed solving Minus' problem as
much as he enjoyed creating it.