25.
If Augustus Cæsar was born September 23, B.C. 63, he celebrated his sixty-third birthday on September 23, B.C. 0; or, writing it otherwise, September 23, A.D. 0; or again, if we wish to include both symbols, B.C. 0 A.D. It is clear that his sixty-second birthday fell on September 23, B.C. 1, and his sixty-fourth on September 23, A.D. 1, so that the intervening year may be written as above.
26.
The difference of the ages of A and B who were born in 1847 and 1874, is 27, or 30 - 03. Hence, when A was 30 B was 03. And A was 30 in 1877. Eleven years later A was 41 and B 14, and eleven years after that A was 52 and B 25. Thus the same two digits served to express the ages of both in 1877, 1888, and 1899. This can only happen in the cases of those whose ages differ by some multiple of nine.
27
A hundred and one by fifty divide,
To this let a cypher be duly applied;
And when the result you can rightly divine,
You find that its value is just one in nine—
is solved by CLIO, one of the nine Muses.