Minus' Solution to

Get in Line, Buddy!
Posted February 10 - 16, 1997

Take left to right to be south to north. The order will then be: 
C  A  M  S
    or
C  M  A  S
Sam is north of Maria.
Sam is north of Arthur, and Arthur is north of Cordelia, so Sam is north of Cordelia.

Therefore, Sam is the northernmost walker.

Maria is south of Sam, but there's no indication whether she or Arthur is the second in line.

Cordelia is the southernmost walker.
Your Solutions

It looks like school is back in session for our Australian friends!

This week's best solution, and meal-time reading, came from Felicity Pearce at St. Hilda's in Western Australia. Fanciful tales will win a shark anytime.

First of all Sam is proving to everyone that he is hot stuff and makes sure he stays in front. He is followed by Maria who is fairly sheep-like and just follows Sam. After Maria comes Arthur who is playing the knight-in-shining-armour to Cordelia, who is extremely unfit and slow, but to enforce his male superiority Arthur stays in front of her. At the lunch break Sam insults Arthur's macho pride by suggesting that he is sticking with Cordelia because he can't hack it. After lunch Sam and Arthur set out to prove to the other that they are the toughest. Sam manages to stay ahead of Arthur. Confronted by this show of machoism Maria and Cordelia have to stick together, but Cordelia always lags a little behind.

P.S. What I am trying to say is that there are two solutions: S,M,A,C or S,A,M,C.

P.P.S They are always heading north. 




Several students from Patricia Field's 7th grade math class at Robert Smalls Middle School (Beaufort, SC), sent in wonderfully thorough solutions for Minus' fickle palate. This dish was served up by Sarah Hayes:  



You think. Sam is north of Maria and Arthur is south of Sam. Cordelia is
south of Arthur and Maria.Then Cordelia has to be last and Sam has to be
first. Arthur or Maria can be in the middle. It never says anything
about Arthur and Maria either south or north of each other.


So, the
answers are: Sam, Maria, Arthur, and Cordelia OR Sam, Arthur, Maria, and
Cordelia.







Selena Goethie, of Robert Smalls Middle School, tempted Minus with this savory solution:



The skiers are skiing. Four of them travel through misty snow cross
country. The correct order is Sam, Maria, Arthur, and Cordelia. Maria is
north of Cordelia and Sam is north of Maria. They could also be skiing
in another order: Sam, Arthur, Maria, and Cordelia.  This is possible
because the order changes, not the direction.








Lauren Deer wasn't going to be out-done by her classmates. So, she cooked up this rib-sticking answer:



When it said Maria was north of Cordelia I knew Maria was ahead of
Cordelia. Next, it said Arthur was south of Sam. So, Sam is ahead of
Arthur.  That meant Cordelia  is last. The last clue is Sam is north of
Maria. So, that meant Sam is first. 

So with that there could be 2 solutions: Sam, Maria, Arthur, and Cordelia OR Sam, Arthur, Maria, and
Cordelia.
		







John Moser [JohnMoser@msn.com], one of Minus' all-time favourite chefs, delighted our mascot with this mouth-watering solution. Minus didn't even add pepper to this one!



SAM, MARIA, ARTHUR, CORDELIA
      
OR

SAM, ARTHUR, MARIA, CORDELIA                                                 
 
Cordelia has a spacial relationship with everyone. Since she is south of 
Authur and Arthur is south of Sam, therefore Cordelia is also south of Sam. 
She is also south of Maria. Conclusion, she is south of everyone.


Sam has a spacial relationship with everyone. Since he is north of Maria and 
Maria is north of Cordelia, therefore Sam is north of Cordelia. He is also 
north of Arthur. Conclusion, he is north of everyone.


Maria and Arthur have no spacial relationship. Therefore they can exchange 
positions and not change any of the other relationships. 


CONCLUSION, THERE ARE TWO POSSIBLE SOLUTIONS!








Mr. T & his Little Texan Einsteins submitted what might well be the most complex solution that...well, Minus has ever had the pleasure of chewing through. Just ever so slightly "over-cooked", guys!


Hey Minus:


Well, we decided to approach this from an "eliminate the distractors" point of view. We first found the permutation of four things taken four at a time (where order matters). This gave us a total of 24 different configurations to examine. We decided, since 24 was a reasonably small sample to work with, that we would make a systematic list of all of the possibilities and then impose the parameters of the problem onto them one-by-one, thus eliminating all combinations that contradicted the parameters given. Our list looked something like this:

ACMS   CAMS   MACS   SACM		
ACSM   CASM   MASC   SAMC
AMCS   CMAS   MCAS   SCAM
AMSC   CMSA   MCSA   SCMA
ASCM   CSAM   MSAC   SMAC	
ASMC   CSMA   MSCA   SMCA


We then applied each of the parameters to this list and we systematically eliminated all but two of our sequences: SMAC   &   SAMC.  


So to conclude, given these criteria, Sam must be first, Cordelia is bringing up the caboose and Arthur and Maria can occupy the internals in either order.


We realize this was overkill for this simple problem. However, we can never turn down an opportunity to use some of our non-algebra problem-solving strategies. 


See ya next week. Expecially if you could really challenge us. Come OOOONNNNN!!!








Other cooks who contributed to Minus' filling meal are (in no particular order because Minus doesn't play favourites, you know!):


Gail Standing-Forsyth [gstan.for@thezone.net]


Diana Gibbons and Dominee Wheatley [St. Hilda's in Western Australia]


Leah Prichard and Susie Blackburn [St. Hilda's]


Annika and Ivana [St. Hilda's]


Cindy and Divya [St. Hilda's]


Sera Lamotte [St. Hilda's]


Frances McGregor and Ann-Maree Mathison [St. Hilda's]


Jess Moncrieff and Gillian Denison [St. Hilda's]












What a feast!

Now, how on earth is Minus going

to squeeze into his itsy-bitsy swim trunks?