Varsity Math, Week 1

Varsity Math, Week 1

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Welcome! You’ve been recruited to train for the Varsity Math squad. Each week, Coach Newton will pose some tough training sessions to get your mind in fighting shape. There will be challenges at three levels: Freshman, Junior Varsity, and Varsity, the toughest of all.  Best of luck working your way up to first string!

UrnTrouble

Instant Interrogation | Freshman
In the orderly town of Logiton, anyone who’s ever committed a crime always lies, and anyone who’s completely innocent always tells the truth. The Medal of Reason has been stolen from Town Hall, and the Logiton Police have rounded up three suspects: Acey, Basie, and Casey. The police have evidence proving that one of the three is the culprit and one is completely innocent of any crime; they are unsure whether the third has ever committed a crime or not, and of course, they don’t know which suspect is which. The interrogation is short and sweet: “I stole the Medal of Reason!” cries out Acey, to which Basie responds, “Darn right he did,” while Casey just sits there sullenly eyeing everyone in the room. “Case closed!” booms the chief of the Logiton Police.
   Who stole the Medal of Reason, and which of the suspects have completely clean records?

Urn Respect | Junior Varsity
Your friend tells you: This is a remarkable urn. It contains only red and black balls. If you reach in and take one ball at random, there’s an equal chance of drawing red or black. So you might think that if you instead take two at random, it’s 50/50 that your balls will match. Well, you’d be wrong — but if they do match, and then you reach your other hand in and take two more, the chances your second pair match each other are 50/50!
   How many balls in your friend’s urn (before you take any out)?

Find more puzzles at varsity.momath.org.