Consider the matrix P ∈ R6×225 whose elements P ij are +1 when (i,j)= (1,24),(1,206),(2,39),(2,207), etc. −1 when (i,j)= (1,11),(2,27),(3,43), ... This game does have a number of theorems known about it, but re-deriving tough theory is not necessary for the problem as stated. The key idea for solving a question like this with a program is the ...

Identify like terms in the expression. Add or subtract the coefficients of like terms. Rewrite the expression with combined terms. Simplify 4x+5−2x+3. Combine the like terms (4x and −2x): 4x−2x=2x. Combine constants (5 and 3; 5 + 3 = 8).

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