Glen, Hao, Ioana, Julia, Karla, and Levi participated in the 2023 Canadian Team Mathematics Contest. On their team uniforms, each had a different number chosen from the list . Hao's and Julia's numbers were even. Karla's and Levi's numbers were prime numbers. Glen's number was a perfect square. What was Ioana's number?
CEMC Pascal
Solution
From the given list, the numbers 11 and 13 are the only prime numbers, and so must be Karla's and Levi's numbers in some order. From the given list, 16 is the only perfect square; thus, Glen's number was 16. The remaining numbers are . Since Hao's and Julia's numbers were even, then their numbers must be 12 and 14 in some order. Thus, Ioana's number is 15.
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