flip all four pancakes
flip the first pancake
flip the first three pancakes
1 2 3 4 David S. Cohen, a writer for the TV show The Simpsons, found that this could be sorted with a maximum of 23n/14 flips. Fortunately, Harry Dweighter discovers that he can use another plate to make his job easier. He can slide pancakes from the first plate onto the second plate (keeping them the same way up), flip pancakes on the first plate in the same way as before and finally slide the pancakes from the second plate back onto the first (keeping them the same way up). For example, if you had the stack , you would slide of the top pancake onto a new plate, flip the top pancake from the original plate and return the pancake that you slid off, producing . The maximum number of flips required with the aid of another plate has also been calculated. Unburnt pancakes require n-1 flips and burnt pancakes require n+1 flips. ‘And why is this useful?’ people have been known to ask. Chromosomes can evolve in the same way a stack of burnt pancakes can be ordered using a second plate. A chromosome is an ordered list of genes. The genes evolve by tiny mutations, however, occasionally whole genes are flipped in the same way pancakes are with a plate. When genes flip with each other, it can quickly make a chromosome look entirely different. By using pancake sorting techniques, it is possible to map how chromosomes are related. To demonstrate how chromosomes are so similar, if we represent genes in mice the same way burnt pancakes are shown, we get .. These genes occur in humans with a permutation of these genes shown to be If we map how DNA evolved from mice to humans, one of the steps will be the common ancestor between these two animals. Want to guess how we know how to get from the mouse chromosome to human chromosome? You guessed it: pancake sorting. Here’s how you can get from mice to men in six steps: (On the following page).
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