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Yash Qualifies for National MathCounts Competition

posted Mar 28, 2013, 9:05 AM by Sarah Winne   [ updated Mar 28, 2013, 12:52 PM ]


Congratulations to Yash.

He came in 4th place as an individual at Maine's MathCounts Competition, earning himself a spot on the State of Maine team that goes to the National Competition in Washington D.C. in May. This is quite an accomplishment for a 7th grader, as most of the competitors are 8th graders.

The 2013 state-level problems have not been released, but here's one from 2012. You have 3 minutes to answer this question; calculators are allowed:

There are 348 students in Jack’s school. Each student’s first and last initials form a unique ordered letter pair. How many more students are required to guarantee that there are two students whose initials form the same ordered letter pair?



Answer: The first and last initials of the 348 students form a unique ordered letter pair. We must find how many more students are required to guarantee that there are two students whose initials form the same ordered letter pair. Since there are  26 letters of the alphabet we can have 26 × 26 = 676 unique combinations. Therefore, we must have 677 students to ensure that two students have the same initials. The number of additional students needed is 677 − 348 = 329 


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