All entries for January 2007

January 29, 2007

Tourist Agency Problem

A tourist agency anonuces an interesting scheme for all tourist who are interested in having a tour of as many cities as possible in europe. Given an initial budget B , tourist agency works as follows.

Given the map of the cities and the prices between the cities are given as a weighted directed graph G = {V, E, p}. There are different cities V = {C_1, C_2, ..., C_n} and from every city there are some flight connections to some other cities (C_i, C_j) \in E and the price of the flights between cities is fixed in advance p(C_i, C_j). Starting from a city C_i and a budget B, tourist agency picks an amount d < B, such that there exists a city C_j such that p(C_i, C_j) = d. If the tourist agency can not choose such a number d and the remaining budget B is greater than 0, then toursit agency agrees to pay a high price as penalty to the tourists and thus toursit agency loses. Otherwise the tourists pick a city such that flight price to the destination city is d unit and take the flight. Tourist agency then updates the budget B to B-d and the tour continues. The aim of the tourist agency is to reach a city with 0 budget.

Given a map and an initial budget, find optimal strategy for the tourist guide and the tourists.


January 02, 2007

students == severely mentally impaired

Properties exempt from council tax

Some property is exempt from council tax altogether. It may be exempt for only a short period, for example, six months, or for a longer time.

Properties which may be exempt are:-

  • property which is empty. It has to be unoccupied and substantially unfurnished. The exemption applies for a maximum of six months and the property has to be vacant for the whole of this period
  • property which is vacant because it needs major repairs or alterations to make it habitable. The exemption applies for a maximum of 12 months whether the work is actually finished or not by then
  • condemned property
  • property which has been re-possessed by a mortgage lender
  • property unoccupied because the person who lived there now lives else where because they need to be cared for, for example, in hospital (or with relatives)
  • property which is unoccupied because the person who lived there has gone to care for someone else
  • any property that only students live in. This may be a hall of residence, or a house
  • a caravan or boat which is used as a main residence but which is unoccupied. This exemption lasts for up to six months. A holiday caravan or boat is exempt if it’s on a property where council tax is paid
  • a property where all the people who live in it are aged under 18
  • a property where all the people who live in it are either severely mentally impaired or are students or where there is a mixture of both
  • a self-contained ‘granny flat’ where the person who lives in it is a dependent relative of the owner of the main property.

PhD Comics

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