Four friends: Dave, Mike, John, and Terry, are nicknamed Stick, Batman, Atomic Head, and Feaser, but not in that order. Which friend has which nickname?

A. John is faster than Batman but not as strong as Atomic Head.
B. Batman is stronger than Terry but slower than Feaser.
C. Dave is faster than both Stick and John, but not as strong as Batman

Strength and speed are independent qualities.

(from Terry Stickels)

Worked SolutionP:
We must assume that if x is fasterslower or strongerweaker than y, that x is not equal to y.
101. [1] John != Batman
102. [1] John != Atomic Head
103. [2] Batman != Terry
104. [3] Dave != Stick
105. [3] Dave != Batman
Thus from this we can conclude:
106. mike's nickname is batman, because none of the others are batman.
Now we know that mike is batman we can examine the statements in more detail. The only nicknames left are (A) "Stick"  (B)"Freaser" and (C)"Atomic Head"
107. John != C [102]
108. Therefore John must be A or B
109. Dave != A [104]
110. Therefore Dave must be B or C
111. Terry can be A, B or C.

Now we are left with two possibilities
1.         Dave = B(Freaser) , John = A(Stick), Terry = C(Atomic Head)
2.         Dave = C(Atomic Head), John =B(Freaser), Terry = B(Stick)
These are the only two possibilities. Any others don't fit with [108,110 & 111] above.

112. Stick is either John or Terry [107 & 111]

113. Atomic Head is either Dave or Terry [110 & 111]

114. Freaser is either Dave or John [108 & 110]

Speed

115. John > Mike
116. Freaser (Dave or John) > Mike
117. Dave > Stick (John or Terry)
118. Dave > John

Strength

119. Atomic Head (Terry or Dave) > John
120. Mike > Terry
121. Mike > Dave

Thus, we conclude that
 
Mike is Batman
John is Freaser
Terry is Stick
Dave is Atomic Head
 
or
 
Mike is Batman
Dave is Freaser
John is Stick
Terry is Atomic Head
 
 
But if we are to assume that Stick and John don't share the idenity relationship then the only valid conclusion we are left with is:

Mike is Batman
John is Freaser
Terry is Stick
Dave is Atomic Head

 

Edited on January 2, 2006, 3:38 am

Edited on January 2, 2006, 3:41 am

Posted by Eamonn on 2005-12-30 03:35:44