One day in December 2015, three 2-digit prime numbers A, B and C, were
given to three members of a High School math team: Ashley, Beth, and Caitlin (respectively).
They had this conversation:
Ashley: you two add your numbers, we get precisely today's date!"
Beth: you two add your numbers, we get my birthday this month, which was before today."
Caitlin: you two add your numbers, we get my birthday this month, which is after today."
What number did Caitlin get?
Correct answer: A
Explanation
The numbers A, B, C belong a priori in the set f11; 13; 17; 19g|Note that the
addition of any of these two 2-digit prime numbers cannot be greater than or equal to 30,
which places a strong restriction on the greatest of the three numbers: this must be at most
19. These are the only valid additions of any two numbers on that set:
11 + 11 = 22, 11 + 13 = 24, 11 + 17 = 29, 11 + 19 = 30, 13 + 13 = 26, 13 + 17 = 30
Note in particular the strict inequalities placed on the addition of any of these two numbers:
22 _<A + C < B + C < A + B _<30
Since C < B, there are only two possibilities for B+C at this point: B = 13,C = 11,B+C =
24, or B = 17,C = 11,B + C = 29.
correct answer A
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