1 February   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Different month? 2013 2012

## The Silver Bar Puzzle

Even silver traders somehow distracted by their plans could be trapped in no-money situations. Like our main character, who was not able to pay his rent to the housekeeper for March,2013. As we know the month has exactly 31 days, so he proposed to his housekeeper this strange advanced-payment scheme.

I should add the name of our main character – Silvestar, which compared to the housekeeper’s name Scrooge, is instantly making him our good character. On the other hand Uncle Scrooge the Housekeeper would put nothing in front him as important as the money themselves. Anyway, that’s another story and unfortunately very common one.

Oh yes, now about the advanced-payment scheme they did. Fortunately Silvestar possessed a silver bar exactly 31 inches long. He proposed to give to Uncle Scrooge exactly 1 inch of his silver bar everyday through the March. Because the silver bar is exactly 31 inches long and March has exactly 31 days, the bar will be sufficient to fulfill this arrangement. At the end of the March Silvestar will gather the money, pay to Uncle Scrooge the rent and take back his silver bar (unfortunately at pieces; silver is not counted, but weighted anyway). If of course the noble silver trader fails to complete his part of the deal, the housekeeper will keep the silver in his possession (maybe greedily laughing on a full-moon night, trying to reassemble the pieces).

What Silvestar thought is - it will be a really hardworking dividing the silver bar to 31 pieces. He pour a hot tea in his silver cup (fortunately we are not involved in dividing the cup between them) and give it some thought. Nothing. Then try harder. Something! What if he gave to Uncle Scrooge 1 inch the first day of March, then again 1 inch of the silver bar the second day of March and instead giving him again 1 inch on the third day of March – he could just take the 2 pieces of 1 inch back from Scrooge and give the old man a whole 3 inches piece. He just invented a way to fulfill his part of the deal with lesser cutting and lesser dividing of the silver bar. Which on the other hand will not only save his efforts in dividing the silver bar on 31 pieces, but defacing his shiny treasure so brutally will be avoided too.

After countless sleepless nights Silvestar invented the best approach to this puzzle. He was astonished by the elegant solution he just discovered.  Your task is to find this solution – what is the optimal/minimum dividing we need in order to complete the deal? How many pieces we need? How many inches long will be each piece? Take your shovel and start digging.

And maybe you are eager to read what happen between Silvestar and Scrooge?
Well,
Silvestar tried to explain.
Scrooge tried to understand.

Solved By: bjars