Divide and Conquer
To avoid disputes among the Knights, Sir Domain: "The Royal Land Surveyor" has been appointed to sub-divide plots of land for the King. Recently Sir Domain was presented with a trianglar plot of land which King Ludwig requested be sub-divided into three pieces of equal size and shape. The King desired to present an equal-sized plot of land to each of his three loyal Knights.After giving it some thought, Sir Domain divided the King's triangular shaped plot into three equal parts (shown in red below):
King Ludwig was very pleased with the solution. A short time after, the King was faced with another dilema. How could he sub-divide a newly acquired "L" shaped plot of land? Being the generous King that he was, King Ludwig wanted to give an equal-sized plot of land to each one of the four knights that helped him acquire it.The King presented this new problem to Sir Domain. The royal surveyor thought about how he could sub-divide the oddly shaped plot of land so that four Knights could share it equally. This problem was a bit harder, but Sir Domain came thru with the solution shown below:
By this point King Ludwig found that he could trust Sir Domain's judgement. Needless to say, the King was very pleased.
Then, one day, the King found himself in the situation of needing to sub-divide a perfectly square piece of land among five of his most loyal Knights. The King summoned Sir Domain to the castle. (When the King needs you... you come to him.) Upon seeing King Ludwig, the royal surveyor knew that another puzzle was at hand. King Ludwig asked Sir Domain to divide the square-shaped piece of land into five equal pieces all having the same size and shape.
The surveyor found the problem quite difficult. He could not put it aside, and he neglected his other work. Sir Domain ended up tearing most of his hair out and they now feed him with a spoon. The King is not pleased... Can you help Sir Domain keep his head (literally!). Please help Sir Domain sub-divide the square plot into five pieces, all exactly the same size and shape. It is possible, but I warn you that there is only one way of doing it.
