Question 472702
Let k be the number of logs in the bottom layer, with


*[tex \LARGE \sum_{i=5}^k i = 5+6+...+k = 2840]


If we add 1+2+3+4 to both sides, we get


*[tex \LARGE \sum_{i=1}^k i = 1+2+...+k = \frac{k(k+1)}{2} = 2850]


*[tex \LARGE k(k+1) = 5700]


Since 5700 = 75*76, we obtain k = 75 through a guess-and-check-ish method. Note that we could use the quadratic formula to solve this, but it is rather tedious. Given that the answer is an integer, the best method would be to find two factors of 5700 that are 1 apart. Also, solving the quadratic k^2 + k - 5700 = 0 by factoring is also pointless since it reduces to the previous problem.