Tuesday, 24 February 2009

A Pancake Day Problem

Shrove Tuesday is a term used in several countries for the day preceding the first day of lent. I learned from Wikipedia that " The word shrove is the past tense of the English verb shrive, which means to obtain absolution for one's sins by way of Confession and doing penance. Thus Shrove Tuesday gets its name from the shriving that English Christians were expected to do prior to receiving absolution immediately before Lent begins.

Shrove Tuesday is the last day of "shrovetide", the English equivalent to the Carnival tradition that developed separately in countries of Latin Europe. The term "Shrove Tuesday" is no longer widely known in the United States outside of Liturgical Traditions, such as the Lutheran, Episcopal, and Roman Catholic Churches. [3][4] because of the increase in many immigrant populations and traditions since the 19th century. "Mardi Gras" is much more widely-used. The festival is widely associated with the eating of foods such as pancakes, and often known simply as Pancake Day, originally because these used up ingredients such as fat and eggs, the consumption of which was traditionally restricted during Lent."

I found out that some call the previous saturday, "Egg Saturday", and the monday before Shrove Tuesday is known as "Collop Monday" (A collop is chunk of meat or fat), and the cool mathword on the Sunday before is "Quinquagesima Sunday" which means the fiftieth day; Easter then, would be the first day in the string.

So here is the problem... I cooked up a bunch (call it n) of pancakes for pancake Tuesday, but the stack was not as neat as I wanted. I really wanted them to be stacked with the largest diameter on bottom and the smallest on top. I decided I wanted to restack them by inserting the spatula into the stack somewhere under the top x of them, and flip them over on top of the n-x below. Using only this process, what is the maximum number of times I would have to flip cakes to get them in my preferred order, no matter how they had been originally stacked?

Now pass the maple syrup someone, please?
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