How far can a stack of n identical blocks be made to hang over the edge of a table? The question dates back to at least the middle of the 19th century and the answer to it was widely believed to be of order log n. However, at SODA’06, Paterson and Zwick constructed n-block stacks with overhangs of order n. Here we complete the solution to the overhang problem, and answer Paterson and Zwick’s pr...

Under 5 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 12.8 5 to 9 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 8.9 10 to 14 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 8.5 15 to 19 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 7.1 20 to 24 years . . . . . . . . . . . . . . . . . . . . . . ...

Plummer-Vinson or Paterson-Kelly syndrome presents as a classical triad of dysphagia, irondeficiency anemia and esophageal webs. Exact data about epidemiology of the syndrome are not available; the syndrome is extremely rare. Most of the patients are white middle-aged women, in the fourth to seventh decade of life but the syndrome has also been described in children and adolescents. The dysphag...

Paterson, Stinson and Wei [2] introduced Combinatorial batch codes, which are combinatorial description of Batch code. Batch codes were first presented by Ishai, Kushilevita, Ostrovsky and Sahai [1] in STOC’04. In this paper we answer some of the questions put forward by Paterson, Stinson and Wei and give some results for the general case t > 1 which were not studied by the authors.