2014 UNCO Math Contest II Problems/Problem 4
On the first slate, the Queen’s jurors write the number . On the second slate they write the numbers and . On the third slate the jurors write , and , and so on, writing integers on the th slate.
(a) What is the largest number they write on the th slate?
(b) What is the sum of the numbers written on the th slate?
(c) What is the sum of the numbers written on the th slate?
(a) We can see that this is simply the 20th triangular number. Thus the answer is (b) From the previous problem, we see that the largest number written on the 20th slate is . Since there are 20 numbers on the 20th slate, the smallest number is . Since the numbers on the plate are consecutive, the answer is (c)
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