Halloween Brain Teaser: Can you guess the answer?
This one's tricky!
At the Halloween Ball, every wizard brought at least one black cat. The organizers want to know how many cats and wizards attended. Unfortunately, the only record they have is a group photo taken as the photographer tripped, and all it shows is feet and paws. A ghost flying over the Ball also snapped a photo but it was midnight and all he captured was the total number of eyes, glowing in the dark. If the photographer counted 196 feet and paws and the ghost tallied 126 eyes, how many wizards and how many black cats were at the Ball?
Scroll down for the answer.
126 eyes = 63 individuals. If all these were wizards, there would be 126 legs. We have 70 legs extra or 35 pairs, which means there must be 35 cats and there must be 63-35=28 wizards.
Cats=35 and Wizards=28.
At the Halloween Ball, every wizard brought at least one black cat. The organizers want to know how many cats and wizards attended. Unfortunately, the only record they have is a group photo taken as the photographer tripped, and all it shows is feet and paws. A ghost flying over the Ball also snapped a photo but it was midnight and all he captured was the total number of eyes, glowing in the dark. If the photographer counted 196 feet and paws and the ghost tallied 126 eyes, how many wizards and how many black cats were at the Ball?
Scroll down for the answer.
126 eyes = 63 individuals. If all these were wizards, there would be 126 legs. We have 70 legs extra or 35 pairs, which means there must be 35 cats and there must be 63-35=28 wizards.
Cats=35 and Wizards=28.
Replies to This Discussion
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Permalink Reply by Gary Stuart on -
For the less intuitive and more mathematical...
Let "c" be the number of cats and "w" be the number of wizards.
Since the total number of cats and wizards is 63 (assuming that they each have 2 eyes), therefore:
Equation 1: c + w = 63
There are 196 legs. Since each cat has 4 legs and each wizard only 2 legs, therefore:
Equation 2: 4c + 2w = 196
Solving for c in Equation 1: c = 63 - w
Substituting c in Equation 2:
4(63- w) + 2w = 196
252 - 4w + 2w = 196
56 = 2w
28 = w
Therefore h = 35
So there were 28 wizards and 35 cats.
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