the pancake number, which is the minimum number of flips required to sort any stack of  pancakes has been shown to lie between  and  (approximately 1.07n and 1.64n,) but the exact value remains an open problem. rolling stock
 
since 2007, services had been provided by class 450 but mostly class 444 electric multiple units. he ran the distance in a time of 11.14 seconds. steam traction was used in the south island for longer than in the north island, and a variety of motive power could be found on any of these trains. even windows mobile came with one. 