Math Problem of the Week - Middle School - Dec. 12, 2021 to Dec. 18, 2021

Middle School: 

Question: A centipede, a glowworm, a grasshopper, and a ladybug all have different faborite foods: curry, hot dogs, noodles, and roast beef. Neither the glowworm nor the grasshopper prefers curry. Neither the centipede nor the ladybug prefers noodles. The ladybug had trouble choosing between hot dogs and noodles as a favorite. The grasshopper almost chose roast beef. Math each bug with its favorite food. 

Answer:  The centipede prefers curry, the glowworm prefers roast beef, the grasshopper prefers noodles, and the ladybug prefers hot dogs.

Solution:  To solve this problem, we eliminate possible favorites with each clue. We eliminate the curry as the favorite for the glowworm and the grasshopper first, then we eliminate the noodles for the centipede and the ladybug. Next, we know the ladybug prefers either hot dogs or roast beef, so she can’t have chosen noodles or curry. That leaves curry for the centipede. Since the ladybug had trouble choosing between hot dogs and noodles, she can’t have chosen roast beef. So, the ladybug likes hot dogs. We know the grasshopper almost chose (and therefore didn’t choose) roast beef, so the grasshopper’s favorite must be the noodles. The only option left for the glowworm is roast beef.