He added, `` If this doesn't work out, the three of you barricade yourself in the house and talk terms with them ''.

If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.

If we cluster together, the redcoats can make an advantage out of it, but there's not a blessed thing they can do with two or three of us except chase us, and we can outrun them ''.

If the Af bond is linear then there are three reasonable positions for the hydrogen atoms: ( 1 ) The hydrogen atoms are centered and hence all lie on a sheet midway between the oxygen sheets ; ;

If three dice are tossed, a trial is one toss of one die and the experiment is composed of three trials.

( One big question: If Colmer was to be purged, what should the House do about the other three senior Mississippians who supported the maverick electors??

If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.

If there are three types of atoms forming the mixture, such as iron, nickel and chromium, then it is called a ternary alloy.

If placing a tile causes three or four chains to merge, then the merger steps are handled between the largest and second-largest chain, then with the third-largest chain, and finally with the smallest chain.

" If you have any sense of humor about your strip — and I had a sense of humor about mine — you knew that for three or four years Abner was wrong.

If appropriate proportions of three primary pigments are mixed, the result reflects so little light as to be called " black ".

If a bubble touches identically-colored bubbles, forming a group of three or more, those bubbles — as well as any bubbles hanging from them — are removed from the field of play, and points are awarded.

If there is no discharge, then all three criteria are needed.

If an account has a credit balance, the amount is copied into column three ( the credit column ).

If a wolf was sighted, the hunter would release a team of two or three borzoi.

If the rider plans a significant amount of hillclimbing, a triple-crank ( three chainrings ) front gear system may be preferred.

If a die leaves the table, the shooter will usually be asked to select another die from the remaining three but can request using the same die if it passes the boxman's inspection.

If three sets are played, the pieces usually go into the opponent's starting corners.

If the offensive team completes 10 yards on their first play, they lose the other two downs and are granted another set of three.

* If the offence fails to make ten yards in three plays, the defence takes over on downs.

If symptoms develop during the acute phase, they usually resolve spontaneously within three to eight weeks in approximately 90 % of individuals.

If these three ligands and the metal ion are in one plane, the isomer is said to be meridional, or mer.

If each pixel on the display actually contains three rectangular subpixels of red, green, and blue, in that fixed order, then things on the screen that are smaller than one full pixel in size can be rendered by lighting only one or two of the subpixels.

If the index finger of the right hand is pointed forward, the middle finger bent inward at a right angle to it, and the thumb placed at a right angle to both, the three fingers indicate the relative directions of the x -, y -, and z-axes in a right-handed system.

If we insert vertices in random order, it turns out ( by a somewhat intricate proof ) that each insertion will flip, on average, only O ( 1 ) triangles – although sometimes it will flip many more.

If v < sub > n </ sub > is the number of vertices of degree n and D is the maximum degree of any vertex,

If all four neighbors of v are different colors, say red, green, blue, and yellow in clockwise order, we look for an alternating path of vertices colored red and blue joining the red and blue neighbors.

If the edge length of a regular octahedron is a, the radius of a circumscribed sphere ( one that touches the octahedron at all vertices ) is

If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and boundary grid points.

( If both planes have the same number of vertices,

If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.

If two intersecting planes pass through its center, then they will subdivide the sphere into four lunes or biangles, the vertices of which all coincide with the antipodal points lying on the line of intersection of the planes.

If there are n vertices in the graph, then each tree has n-1 edges.

If G has finitely many vertices, say n of them, then the above statements are also equivalent to any of the following conditions:

If all vertices in a tree are within distance one of a central path subgraph, then the tree is a caterpillar tree.

If all vertices are within distance two of a central path subgraph, then the tree is a lobster.

* If we ignore isolated vertices, which will each be their own component of the minimum spanning forest, V ≤ E + 1, so log V is O ( log E ).

If a mesh covers more pixels in screen space than it has vertices, interpolating colour values from samples of expensive lighting calculations at vertices is less processor intensive than performing the lighting calculation for each pixel as in Phong shading.

If n is even there are n / 2 axes of symmetry connecting the midpoints of opposite sides and n / 2 axes of symmetry connecting opposite vertices.

Putting any of the four vertices in the role of O yields four such identities, but in a sense at most three of them are independent: If the " clockwise " sides of three of them are multiplied and the product is inferred to be equal to the product of the " counterclockwise " sides of the same three identities, and then common factors are cancelled from both sides, the result is the fourth identity.

For example, given a graph G =( V, E ), the shortest path p from a vertex u to a vertex v exhibits optimal substructure: take any intermediate vertex w on this shortest path p. If p is truly the shortest path, then the path p < sub > 1 </ sub > from u to w and p < sub > 2 </ sub > from w to v are indeed the shortest paths between the corresponding vertices ( by the simple cut-and-paste argument described in CLRS ).

If P has trilinear coordinates p: q: r, then the vertices L, M, N of the pedal triangle of P are given by

If G is a connected graph with infinitely many vertices such that every vertex has finite degree ( that is, each vertex is adjacent to only finitely many other vertices ) then G contains an infinitely long simple path, that is, a path with no repeated vertices.

If repeated vertices are allowed, it is more often called a closed walk.