$\mathrm{Four \ positive \ integers \ A, \ B, \ C \ and \ D \ have \ a \ sum \ of \ 36. \ If} \ A+2 \ = \ B-2 \ = \ C+2 \ = \ D+2, \mathrm{what \ is \ the \ value \ of \ the \ product \ ABCD?}$

Since A + 2 = C + 2 = D + 2, A = C = D.

Since A + 2 = B - 2, B = A + 4.

Then A + (A + 4) + A + A = 36. i.e., A = 8.

Then A = C = D = 8 and B = 12. ABCD = 8^3 * 12 = 6144.