Consider the subset sum problem, an example of a problem that is easy to verify, but whose answer may be difficult to compute.

Consider a problem that has these four properties:

Consider the two-dimensional problem introduced above:

Consider, for example, the Closest pair problem:

:: • Consider whether a proposed improvement will solve the problem, or cause " crash migration.

Consider the problem of finding solutions of the form ƒ ( r, θ, φ ) = R ( r ) Y ( θ, φ ).

Consider the problem of factoring the polynomial

Consider the following problem.

Consider a simple 1D advection problem defined by the following partial differential equation

Consider the problem of a mine owner who must decide at what rate to extract ore from his mine.

Use your experience: Consider the problem and try to make sense of it.

Consider the following stochastic programming problem

Consider a problem that can be solved using a recursive algorithm such as the following:

Consider a complex, real-world problem, like those of marketing or making policies for a nation, where there are many governing factors, and most of them cannot be expressed as numerical time series data, as one would like to have for building mathematical models.

Consider the initial value problem

Consider the following problem in deterministic optimal control over the time period:

Consider the unconstrained optimization problem.

Consider the circuit minimization problem: given a circuit A computing a Boolean function f and a number n, determine if there is a circuit with at most n gates that computes the same function f. An alternating Turing machine, with one alternation, starting in an existential state, can solve this problem in polynomial time ( by guessing a circuit B with at most n gates, then switching to a universal state, guessing an input, and checking that the output of B on that input matches the output of A on that input ).

Consider the problem of estimating the probability that a test point in N-dimensional Euclidean space belongs to a set, where we are given sample points that definitely belong to that set.

Consider the general problem of inferring a distribution for a parameter θ given some datum or data x.

Consider the problem of distributing objects given by a generating function into a set of n slots, where a permutation group G of degree n acts on the slots to create an equivalence relation of filled slot configurations, and asking about the generating function of the configurations by weight of the configurations with respect to this equivalence relation, where the weight of a configuration is the sum of the weights of the objects in the slots.

Consider region D in the plane: a unit circle or general polygon — the asymptotics of the problem, which are the interesting aspect, aren't dependent on the exact shape.

Consider for example determining which of the following are to be considered diseases ( i. e., abnormal states requiring cure ): alcoholism, homosexuality, and chronic fatigue syndrome.

Consider this snippet of C code as an example of the ambiguity encountered when determining SLOC:

Consider an equity index.

Consider a nominal value ( say of an hourly wage rate ) in each different year t. To derive a real-value series from a series of nominal values in different years, divide nominal value in each year by P < sup > t </ sup >, the price index in that year.

Consider a light source, Σ, and a light " receiver ", S, both of which are extended surfaces ( rather than differential elements ), and which are separated by a medium of refractive index n that is perfectly transparent ( shown ).

Consider an infinitesimal area, dS, immersed in a medium of refractive index n crossed by ( or emitting ) light inside a cone of angle α.

Consider the cartesian product of topological spaces, indexed by some index.

Consider an unsorted database with N entries.

Consider a database that records customer orders, where an order is for one or more of the items that the enterprise sells.

Consider a dataset represented as a matrix ( or a database table ), such that each row represents a set of attributes ( or features or dimensions ) that describe a particular instance of something.

Consider a database of sales, perhaps from a store chain, classified by date, store and product.

Consider a raffle where a single ticket wins a prize of all entry fees: if the prize is $ 1, the entry fee will be 1 / number of tickets.

Consider the entry corresponding to a particular region and crossing.

Consider adopting a system of holidays in which time off is granted with an eye to minimum inconvenience to the operation of the plant.

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.

( Consider 1 / 0, which is defined with the value of infinity, vs. 0 / 0, which is undefined.

Consider a car's cruise control, which is a device designed to maintain vehicle speed at a constant desired or reference speed provided by the driver.

Consider Japan, for instance, which used to have optional jury trials for capital or other serious crimes between 1928 and 1943.

Consider the case in which liquid crystal molecules are aligned parallel to the surface and an electric field is applied perpendicular to the cell as in the following diagram.

Consider a binary electrolyte AB which dissociates into A + and B-ions and the equilibrium state is represented by the equation:

Consider a hypothetical event which has 8 possible outcomes, in a country using a decimal currency such as dollars.

Consider two ISPs, A and B, which each have a presence in New York, connected by a fast link with latency 5 ms ; and which each have a presence in London connected by a 5 ms link.

Consider the analogy between the sentence " Snow is white " and the character named Snow White, both of which can be true in some sense.

Consider a system in which voters can vote for any candidate from any one of many parties ; suppose further that if a party gets 15 % of votes, then that party will win 15 % of the seats in the legislature.

Consider a traveling transverse wave ( which may be a pulse ) on a string ( the medium ).

Consider Hawaiian, which has a and, but no or.

Consider a hypothetical hotel with countably infinitely many rooms, all of which are occupied – that is to say every room contains a guest.

Consider a customer purchasing an item which costs five pence, who possesses several silver sixpence coins.

Consider a typical rational number 415 / 93, which is around 4. 4624.

Consider the implication " if I am in Massachusetts, then I am in North America ", which we might alternatively express as, " if I were in Massachusetts, then I would be in North America ".

Consider an operation like vector addition, which is used very often in computer graphics applications.

As a sidenote, the fact that artificial intelligences are accepted as citizens of the Culture was a major factor in the Idiran-Culture War, which is explored in Consider Phlebas.

Consider the following claim: " it is false that A and B are both true ", which is written as: