In the first edition (vol. ii. p. 370) I gave a logical problem involving six terms, and requested readers to discover the laws governing the combinations given. I received satisfactory replies from readers both in the United States and in England. I formed the combinations deductively from four laws of correction, but my correspondents found that three simpler laws, equivalent to the four more complex ones, were the best answer; these laws are as follows: a = ac, b = cd, d = Ef.

In case other readers should like to test their skill in the inductive or inverse problem, I give below several series of combinations forming problems of graduated difficulty.

Problem I.

Problem II.

Problem III.

Problem IV.