Robot Duelers

Logic Level 2

Four robots, called A, B, C, and D, are masters at fighting. They each have one main weakness, however, which is the weapon owned by another robot. Here are your clues to solve the question, shown later in the paragraph and in bold text. Number 1, no robot is weak to their own weapon. Number 2, no two robots have the same weakness. Number 3, no robot has more than one weakness. Number 4, if one robot is weak to another robot, then the other robot can't be weak to the first robot. (Example: If A is weak to B, then B can't be weak to A) Number 5, A is weak to the robot that's weak to D. Number 6, C is weak to the robot that's weak B. Number 7, A isn't weak to B. What robot is B weak to? (Also comment the weakness of the three other robots, and if you get it right, share your solution.)

B A D C

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2 solutions

U s i n g \mathbf{Using} t h e \mathbf{the} c l u e s : \mathbf{clues:} \\ 1. A {\color{#D61F06} A} isn't weak to B {\color{#3D99F6} B} and A {\color{#D61F06} A} is weak to the robot weak to D {\color{#20A900} D} (not D {\color{#20A900} D} itself) meaning A {\color{#D61F06} A} is weak to the leftover robot, C {\color{#CEBB00} C} . \\ 2. C {\color{#CEBB00} C} is weak to the robot weak to B {\color{#3D99F6} B} (not B {\color{#3D99F6} B} itself) and A {\color{#D61F06} A} isn't weak to B {\color{#3D99F6} B} , meaning the leftover robot, D {\color{#20A900} D} , is weak to B {\color{#3D99F6} B} \\ 3. As C {\color{#CEBB00} C} is weak to the robot weak to B {\color{#3D99F6} B} and we know D {\color{#20A900} D} is weak to B {\color{#3D99F6} B} , C {\color{#CEBB00} C} is weak to D {\color{#20A900} D} \\ 4. We have not determined who A {\color{#D61F06} A} is the weakness to, and B {\color{#3D99F6} B} is the only robot without a yet determined weakness, meaning B {\color{#3D99F6} B} is weak to A {\color{#D61F06} A} (the answer) \\

A {\color{#D61F06} A} is weak to C {\color{#CEBB00} C} who is weak to D {\color{#20A900} D} who is weak to B {\color{#3D99F6} B} who is weak to A {\color{#D61F06} A}

Vishruth K
Mar 18, 2021

A cannot be weak to A, B can't be weak to B, C can't be weak to C, and D can't be weak to D, shown in clue 1. Clue 5 tells us that A can't be weak to D because A can't be weak to A which is weak to D, nor can A be weak to D who is weak to D. Clue 6 tells us that C can't be weak to B because C can't be weak to C which is weak to B, nor can C be weak to B which is weak to B. Clue 7 tell's us A isn't weak to B, so A must be weak to C. Now, the only person who can be weak to B is D. Finally, we can fill in the blanks in clues 5 and 6. Since A is weak to C, C must be weak to D. Finally, C is weak to D, so D must be weak to B. (You might have not included the 2nd to last step, which is fine and also produces a correct answer to the asked question.)

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