MathDB

8

Part of 2018 MIG

Problems(2)

2018 Individual #8

Source:

5/6/2022
The set of natural numbers are arranged as so: 12345678910111213141516171819202122232425⋮\begin{array}{ccccccccc} & & & & 1 & & & &\\ & & & 2 & 3 & 4 & & &\\ & & 5 & 6 & 7 & 8 & 9 &\\ & 10 & 11 & 12 & 13 & 14 & 15 & 16 &\\ 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 & 25\\ & & & & \vdots & & & & \end{array}
so that each row has 22 more numbers in it, and the rows are centered. What is the number under 4949?
<spanclass=′latex−bold′>(A)</span>60<spanclass=′latex−bold′>(B)</span>61<spanclass=′latex−bold′>(C)</span>62<spanclass=′latex−bold′>(D)</span>63<spanclass=′latex−bold′>(E)</span>64<span class='latex-bold'>(A) </span>60\qquad<span class='latex-bold'>(B) </span>61\qquad<span class='latex-bold'>(C) </span>62\qquad<span class='latex-bold'>(D) </span>63\qquad<span class='latex-bold'>(E) </span>64
2018 Individual
2018 Team #8

Source:

1/18/2023
A marathon runner has a very peculiar way of training for a marathon. On the first day of week 11, the runner runs a distance equivalent to the first prime number. On the second day, the runner runs a distance equal to the second prime number, continuing this pattern until the 77th day of the week. Each successive week, the runner runs one more mile per day than they did on the same day of the previous week. The runner continues this process until the average distance run each week exceeds the distance of a marathon (26.226.2 miles). How many weeks does the marathoner train?
2018 Team