South Carolina High Energy Mathematics Teachers' Circle Problems from the Fourth Workshop Session

 The square root of 4,356 is an integer. Without a calculator, determine what that integer is by eliminating possibilities. Then do the same for 8,464. Who is lying? Jim tells lies on Fridays, Saturdays, and Sundays. He tells the truth on all other days. Melanie tells lies on Tuesdays, Wednesdays, and Thursdays. She tells the truth on all other days. If they both say "Yesterday I lied," then what day is it today? Down on the Farm Gordon and Pearl lived on a farm in Kansas with their father, Emil, and their mother, Olive. One day Gordon asked his father, "Dad, what happened to that cat I used to have?" Pearl, overhearing this, said, "Yeah, and I used to have a horse. Where is she?" Emil replied, "Gordon's tomcat and Pearl's old nag were not much use. I traded them for my new goat." Olive then said, "Hey, that sounds like a good cryptarithmetic problem. Let's see if we can solve it." She wrote down GTOM + PNAG = EGOAT. Each letter stands for a different digit, 0 through 9. No two letters stand for the same digit. Determine which digit each letter represents. There are two clues: G = 5 and A represents an odd digit. Denise was having an argument with her roommate, Frankie, about whether or not Frankie could cook. After arguing for a while, Denise said, "Wow, wow, so cook!" Frankie, who was a math teacher, noticed that what Denise said might be a cryptarithm. She sat down to work on it, and Denise ended up cooking dinner. Each letter in the cryptarithm stands for a different digit. (Hint: K = 9)