(2) In terms of meaning, (n +3)(n+2) = 506.

Solution: n 1 =-25 (truncated) n2 =20.

(3) White ceramic tile: 20×(20+1)= 420 (block)

Therefore, * * * needs black tiles: 506-420 = 86 (blocks).

In question (2), the cost of purchasing ceramic tiles is 420×3+86×4 = 1604 (yuan).

(4)n(n+ 1)= N2+5n+6-n(n+ 1)。

The solution is 33 with n = 3√2.

Because n is not an integer.

The number of black and white tiles varies.