Problem of the Fortnight #1
Royal
Games
Once upon a time an aged king, nearing the end of his days and having no heir to succeed him upon the throne, cast about him for a worthy successor. In all corners of his kingdom he caused search to be made for young men of promise. These he gathered together by districts for further judging and selection, and so again and again until the four most gifted men of the country were determined and brought before him for a final choice. So near alike in their capabilities were they that no ordinary test could mark one as superior to his companions, and in order to make his final decision the king devised the following scheme.
The four were tightly blindfolded and seated around the table. While seated thus the king said to them, “In a moment I shall make a mark upon each of your foreheads. Perhaps the mark will be black and perhaps the mark will be white. I shall then cause your blindfolds to be removed, allowing you to look upon the foreheads of your companions. Those of you who see more black marks than white upon your companions will stand and remain standing until such time as one of you can state convincingly the color of the mark he bears. That one I shall name my successor.
According to his word the king marked each man upon the forehead. When the blindfolds were removed each man looked at his fellows and at once arose. For many minutes each stood silent, pondering. Finally one man spoke, saying “Sire, I bear a black mark,” and straightaway gave convincing argument for his assertion.
How did the king actually mark the men, and
how did the successful candidate prove the existence of a black mark upon his
forehead?
Solutions are due by