Jump to content
BrainDen.com - Brain Teasers

Templeton

Members
  • Content Count

    1
  • Joined

  • Last visited

Community Reputation

0

About Templeton

  • Rank
    Newbie
  1. Templeton

    For a given NxN square there are N diagonals, starting with N in the top right corner. Each number in the sequence is below and one to the left of the previous number. So it is N - 1 more than the previous number. For a given N this forms an arithmetic progression with d = N -1. So S = (n/2) (2a + (n-1)d) where S = 5335, n = N, a = N, d = N - 1 Substitute in and arrange to get: N3 + N = 10670 Solve for N and find N2 for the bottom right entry. This equation is a depressed cubic (no N2 term) and can be solved by the Cardano method ( http://www.sosmath.com/algebra/factor/fac11/fac11.html ) to give N = 22. Alternatively, note that, for N much greater than 10, N is less than 1% of N3 and can be ignored. This gives N3 ~ 10670 N ~ 22 So the bottom right entry is 222 = 484
×
×
  • Create New...