Ambassadors from countries A, B, C, D, E, and F are to be seated around a circular conference table. Friendly relations among the various countries are described as follows: A has friendly relations with B and F. B has friendly relations with A, C, and E. C has friendly relations with B, D, E, and F. E has friendly relations with B, C, D, and F . All friendly relations are mutual. Using vertices to represent countries and edges to represent friendly relations, draw a graph that models the information given. Then use a Hamilton circuit to devise a seating arrangement around the table so that the ambassadors from B and E are seated next to each other, and each ambassador represents a country that has friendly relations with the countries represented by the ambassadors next to him or her.
Ambassadors from countries A, B, C, D, E, and F are to be seated around a circular conference table. Friendly relations among the various countries are described as follows: A has friendly relations with B and F. B has friendly relations with A, C, and E. C has friendly relations with B, D, E, and F. E has friendly relations with B, C, D, and F . All friendly relations are mutual. Using vertices to represent countries and edges to represent friendly relations, draw a graph that models the information given. Then use a Hamilton circuit to devise a seating arrangement around the table so that the ambassadors from B and E are seated next to each other, and each ambassador represents a country that has friendly relations with the countries represented by the ambassadors next to him or her.
Ambassadors from countries A, B, C, D, E, and F are to be seated around a circular conference table. Friendly relations among the various countries are described as follows: A has friendly relations with B and F. B has friendly relations with A, C, and E. C has friendly relations with B, D, E, and F. E has friendly relations with B, C, D, and F. All friendly relations are mutual. Using vertices to represent countries and edges to represent friendly relations, draw a graph that models the information given. Then use a Hamilton circuit to devise a seating arrangement around the table so that the ambassadors from B and E are seated next to each other, and each ambassador represents a country that has friendly relations with the countries represented by the ambassadors next to him or her.
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
2
p-1
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
23
The set T is the subset of these residues exceeding
2°
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
how come?
Shading a Venn diagram with 3 sets: Unions, intersections, and...
The Venn diagram shows sets A, B, C, and the universal set U.
Shade (CUA)' n B on the Venn diagram.
U
Explanation
Check
A-
B
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3. A different 7-Eleven has a bank of slurpee fountain heads. Their available flavors are as follows: Mountain
Dew, Mountain Dew Code Red, Grape, Pepsi and Mountain Dew Livewire. You fill five different cups full
with each type of flavor. How many different ways can you arrange the cups in a line if exactly two Mountain
Dew flavors are next to each other?
3.2.1
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