Strange Signs
---------- To A -- To B -- To C -- To D
Sign A ---- X ----- 20 ---- 19 ----- 17
Sign B ---- 19 ----- X ---- 18 ----- 15
Sign C ---- 19 ---- 18 ----- X ----- 20
Sign D ---- 17 ---- 19 ---- 20 ----- X
The table above shows the distances (km) given on signposts at four villages A, B, C, and D to their three neighboring villages. For example, at village B the signpost gives a distance of 19km to village A. Each signpost has exactly three numbers on it. The trouble is, the signposts have been vandalized so that only sign gives exactly three correct distances, one gives precisely two correct, one has exactly one correct one correct, and one has no correct distances. When the signposts were correct, no distance between two villages was repeated between another pair of villages.
State the number of correct distances on each sign!
Sign A ---- X ----- 20 ---- 19 ----- 17
Sign B ---- 19 ----- X ---- 18 ----- 15
Sign C ---- 19 ---- 18 ----- X ----- 20
Sign D ---- 17 ---- 19 ---- 20 ----- X
The table above shows the distances (km) given on signposts at four villages A, B, C, and D to their three neighboring villages. For example, at village B the signpost gives a distance of 19km to village A. Each signpost has exactly three numbers on it. The trouble is, the signposts have been vandalized so that only sign gives exactly three correct distances, one gives precisely two correct, one has exactly one correct one correct, and one has no correct distances. When the signposts were correct, no distance between two villages was repeated between another pair of villages.
State the number of correct distances on each sign!
posted by Zaux at
1:00 PM
1 Comments:
Strange Signs
Given:
A B C D
A X 20 19 17
B 19 X 18 15
C 19 18 X 20
D 17 19 20 X
1 sign has 0 true, 1 sign 1 true, 1 sign 2 true, 1 sign 3 true,
no distance between two villages was repeated between another pair of villages
-If distance from x to y= z then distance from y to x =z
-eliminate duplicate numbers
T=true, F=False
IF A is true
A B C D #TRUE
A X T T T 3
B F X 18 15 1,2
C T 18 X 20 1,2,3
D T F F X 1
No 0 possible
IF B is true
A B C D #TRUE
A X F F 17 0,1
B T X T T 3
C F T X 20 1,2
D 17 F 20 X 0,1,2
IF 17&20 are true A=1,C=2,D=2
IF 17 is true, but 20 is false A=1,C=1,D=1
IF 17 is false but 20 ist true A=0,C=2,D=1
IF 17&20 are false A=0,C=1,D=0
IF C is true
A B C D #TRUE
A X F T 17 1,2
B F X T 15 1,2
C T T X T 3
D 17 F T X 1,2
No 0 possible
IF D is true
A B C D #TRUE
A X F F T 1
B F X 18 F 0,1
C F 18 X T 1,2
D T T T X 3
if 18 is true, B=1, C=2
if 18 is false B=0, C=1
From B is true, we choose 17 is false but 20 is true
giving
Answer:
Sign A 0 correct
Sign B 3 correct
Sign C 2 correct
Sign D 1 correct
Hopefully no mistakes
Cam
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