What theorems and principles are employed to solve the following riddle: Ten band members have had their musical instruments placed randomly within boxes. Each band member gets five shots at opening boxes, trying to find their own instrument. (Thus, a 50% chance of each individual finding the desired instrument.) They're not allowed to communicate about what they find. If the entire band fails to find their instruments, they're all fired...and the odds of them all finding their instruments via random guessing is 1 in 1,024. But the drummer has an idea that will radically increase their odds of success. What theorems and principles would you need to employ to solve the riddle. Solving the riddle is not the question. What are the methods (proof by contraposition, would be an example) Rules : • Instruments have been randomly placed in 10 boxes. • The pictures on the boxes don't necessarily correspond to the instruments inside. • Each musician can open up to 5 boxes, and they have to close all of the boxes they open. • All ten musicians must find their own instruments. • The musicians can't communicate to each other what they find.
What theorems and principles are employed to solve the following riddle:
Ten band members have had their musical instruments placed randomly within boxes. Each band member gets five shots at opening boxes, trying to find their own instrument. (Thus, a 50% chance of each individual finding the desired instrument.) They're not allowed to communicate about what they find. If the entire band fails to find their instruments, they're all fired...and the odds of them all finding their instruments via random guessing is 1 in 1,024. But the drummer has an idea that will radically increase their odds of success. What theorems and principles would you need to employ to solve the riddle.
Solving the riddle is not the question. What are the methods (proof by contraposition, would be an example)
Rules :
• Instruments have been randomly placed in 10 boxes.
• The pictures on the boxes don't necessarily correspond to the instruments inside.
• Each musician can open up to 5 boxes, and they have to close all of the boxes they open.
• All ten musicians must find their own instruments.
• The musicians can't communicate to each other what they find.
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