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Hockey Score Settlement (Posted on 2014-02-03) Difficulty: 3 of 5
Three teams A, B and C participated in a 3 sided hockey tournament. In three games, team A played team B, team B played against team C, and team A played against team C.
  1. The three final scores of the games consisted of the numbers 1, 2, 3, 4, 5, and 6.
  2. The difference between the team Aís higher score and the team B's higher score was one more than the difference between team Bís lower and team Cís lower score.
  3. The highest total of a teamís two scores was achieved by the team that lost the greatest number of games.
Which team achieved the highest total of its two scores?

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution computer solution Comment 2 of 2 |
DECLARE SUB permute (a$)
CLS
s$ = "123456": h$ = s$
' "abbcac"
DO
a1 = VAL(MID$(s$, 1, 1))
a2 = VAL(MID$(s$, 5, 1))
b1 = VAL(MID$(s$, 2, 1))
b2 = VAL(MID$(s$, 3, 1))
c1 = VAL(MID$(s$, 4, 1))
c2 = VAL(MID$(s$, 6, 1))
IF a1 > a2 THEN ahi = a1: ELSE ahi = a2
IF b1 > b2 THEN bhi = b1: blo = b2: ELSE bhi = b2: blo = b1
IF c1 > c2 THEN clo = c2: ELSE clo = c1
IF ABS(ahi - bhi) = 1 + ABS(blo - clo) THEN
atot = a1 + a2
btot = b1 + b2
ctot = c1 + c2
hitot$ = ""
IF atot > btot AND atot > ctot THEN hitot$ = "a"
IF btot > atot AND btot > ctot THEN hitot$ = "b"
IF ctot > btot AND ctot > atot THEN hitot$ = "c"
awon = 0: bwon = 0: cwon = 0
IF a1 > b1 THEN awon = awon + 1: ELSE bwon = bwon + 1
IF a2 > c2 THEN awon = awon + 1: ELSE cwon = cwon + 1
IF b2 > c1 THEN bwon = bwon + 1: ELSE cwon = cwon + 1
lowon$ = ""
IF awon < bwon AND awon < cwon THEN lowon$ = "a"
IF bwon < awon AND bwon < cwon THEN lowon$ = "b"
IF cwon < bwon AND cwon < awon THEN lowon$ = "c"
IF hitot$ = lowon$ AND hitot$ > "" THEN
PRINT hitot$, MID$(s$, 1, 2); " "; MID$(s$, 3, 2); " "; MID$(s$, 5, 2),
PRINT atot; btot; ctot, awon; bwon; cwon
END IF
END IF

permute s$
LOOP UNTIL s$ = h$

finds
                 game           tot          games 
                scores         points         won 
               AB BC AC       A  B  C       A  B  C 
 c             12 43 65       7  6  8       1  2  0 

meaning C achieved the highest total score. A lost to B 1-2; B won against C 4-3 and A won against C 6-5. A had a total of 7 points; B, 6 and C, 8, for respective numbers of wins of 1, 2 and 0.

Edited on February 3, 2014, 1:31 pm
  Posted by Charlie on 2014-02-03 13:22:32

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