IMO 1979 LL BRA7
M = (ai,j), i, j = 1, 2, 3, 4, is a square matrix of order four.
IMO 1979 LL BRA7
Origin: BRA
Problem
M = (ai,j), i, j = 1, 2, 3, 4, is a square matrix of order four. Given that: (i) for each i = 1, 2, 3, 4 and for each k = 5, 6, 7, ai,k = ai,k−4; Pi = a1,i + a2,i+1 + a3,i+2 + a4,i+3; Si = a4,i + a3,i+1 + a2,i+2 + a1,i+3; Li = ai,1 + ai,2 + ai,3 + ai,4; Ci = a1,i + a2,i + a3,i + a4,i, (ii) for each i, j = 1, 2, 3, 4, Pi = Pj, Si = Sj, Li = Lj, Ci = Cj, and (iii) a1,1 = 0, a1,2 = 7, a2,1 = 11, a2,3 = 2, and a3,3 = 15; find the matrix M.