% Change

From the 2013 South Africa Olympiad:

A is a 2-digit number and B is a 3-digit number such that A increased by B% equals B reduced by A%. Find all possible pairs (A, B).



William and his words

I had a very enjoyable bank holiday weekend, one highlight of which was finally cracking a problem that had caught my eye months ago but had been left unattempted until the aforementioned weekend. For now I will simply post the problem statement – it is one of the strangest puzzles I have ever come across and is definitely worth thinking about before looking at a solution.

From the 2007 Tournament of the Towns:

For each letter in the English alphabet, William assigns an English word which contains that letter. His first document consists only of the word assigned to the letter A. In each subsequent document, he replaces each letter of the preceding document by its assigned word. The fortieth document begins with “Till whatsoever star that guides my moving.” Prove that this sentence reappears later in this document.