Original Puzzle.

Slides:



Advertisements
Similar presentations
Spreadsheet Vocabulary
Advertisements

CSE 421 Algorithms Richard Anderson Lecture 23 Network Flow Applications.
ENGR-1100 Introduction to Engineering Analysis
B) it can be used to solve indeterminate trusses
Do Now Pass out calculators. Solve the following system by graphing: Graph paper is in the back. 5x + 2y = 9 x + y = -3 Solve the following system by using.
3.5 Solving systems of equations in 3 variables
5.3 Solving Systems using Elimination
Systems of Linear Equations Block 44. System of Linear Equations A system of equations is a set or collection of equations that you deal with all together.
 The factorial function (n!)  Permutations  Combinations.
Box Method for Factoring Factoring expressions in the form of.
MAC 1140 Unit 4 Test Review. 1. Give the order of the following matrix:.
Elimination Link to video. Example: Find the P.O.I. by elimination for and Steps Example 1a. Rearrange one (or both) of the equations so that the x’s.
MATH 3581 — College Geometry — Spring 2010 — Solutions to Homework Assignment # 3 B E A C F D.
Algebra-2 Section 3-2B.
Ch X 2 Matrices, Determinants, and Inverses.
Dr. Fowler CCM Solving Systems of Equations By Elimination – Harder.
Computing Science 1P Large Group Tutorial 20 Simon Gay Department of Computing Science University of Glasgow 2006/07.
Solving Systems of Equations Algebraically STEPS: 1.Solve for a variable in either equation. Get variable alone (x or y) 2.Substitute for this variable.
HandoutMay 2007Task Scheduling A Lecture in CE Freshman Seminar Series: Ten Puzzling Problems in Computer Engineering.
Solving a system of equations by adding or subtracting.
Systems of Equations: Elimination, Part II Unit 7, Lesson 5b.
Triangle Centres. Mental Health Break Given the following triangle, find the:  centroid  orthocenter  circumcenter.
Computing the Cross Product The formula to compute the cross product is a complex one when vectors are in Cartesian form: if u = [a, b, c] and v = [d,
1.3 Solving Systems by Substitution. Steps for Substitution 1.Solve for the “easiest” variable 2.Substitute this expression into the other equation 3.Solve.
5.2: Solving Systems of Equations using Substitution
7.4. 5x + 2y = 16 5x + 2y = 16 3x – 4y = 20 3x – 4y = 20 In this linear system neither variable can be eliminated by adding the equations. In this linear.
Step 1: Place x 2 term and constant into the box 2x 2 2 PROBLEM: 2x 2 + 5x + 2.
AES Encryption FIPS 197, November 26, Bit Block Encryption Key Lengths 128, 192, 256 Number of Rounds Key Length Rounds Block.
Su Doku!. Given a grid and some numbers, fill the rest in… They might be in the wrong order…
By Meli & Amy & Meggie & Bex. What is route inspection hmmmm??? Objective: Is to go along every single edge and end up back to where you started from.
7-3: Solving Systems of Equations using Elimination
Solving systems of equations with three variables January 13, 2010.
Adding two numbers together which have the same absolute value but are opposite in sign results in a value of zero. This same principle can be applied.
Chapter 1 Section 1.6 Algebraic Properties of Matrix Operations.
Elementary Row Operations Interchange two equations Multiply one equation by a nonzero constant Add a multple of one equation to another equation.
Box Method for Factoring Factoring expressions in the form of.
南亚和印度.
Solving Systems of Equation Using Elimination. Another method for solving systems of equations Eliminate one of the variables by adding the two equations.
Elimination Method - Systems. Elimination Method  With the elimination method, you create like terms that add to zero.
$200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200.
December 12, 2011 By the end of today: I will know how to solve systems by elimination.
Elementary Matrix Theory
Warmups – solve using substitution
Box Method for Factoring
Box Method for Factoring
10.5 Inverses of Matrices and Matrix Equations
Solving Systems of Equations using Elimination
Geometry 5-4 Midsegments
Block LU Decomposition: explained
Solve Systems of Equations by Elimination
3.5 Solving systems of equations in 3 variables
Topic 6: Multiplication
Fractional Factorial Design
Systems of Linear Equations and Problem Solving
Synthesis and Verification of Finite State Machines
AB AC AD AE AF 5 ways If you used AB, then, there would be 4 remaining ODD vertices (C, D, E and F) CD CE CF 3 ways If you used CD, then, there.
Addendum to Chapter 14 Tue, Apr 25, 2006
Solving Linear Systems by Linear Combinations (Elimination)
Solving Systems of Equations by the Substitution and Addition Methods
Addendum to Chapter 14 Tue, Apr 25, 2006
Systems with Three Variables
Mathematical Trickery
Warm Up Solve by graphing Solve by substitution.
6.3 Using Elimination to Solve Systems
Mixed Numbers Equivalent Simplest Form Comparing
Bellwork: 1. Write a two-column proof for the following theorem:
Solving Systems by ELIMINATION
Solving Systems of Equations by Substitution
Homework Solutions.
Presentation transcript:

Original Puzzle

F6 8 (C5,D2,E9)

G8 8 (B7,E9,H1)

I4 8 (C5,F6,G8)

A3 8 (B7,C5,H1)

E2 4 (D9,E4)

D1 1 (E6,F5,H1)

C2 1 (B9,H3)

D3 6 (A2)

F2 5 (what's left in box)

F5 6 (D3,E7)

D5 3 (C4,E3)

I9 6 (C8,E7,H4)

G1 6 (D6,H4,I9)

G3 2 (Phan 2's H5/6, I8)

I3 5 (C1,F2)

I1 4 (E2)

B2 2 (F1,G3) Hard part, Phantom 5,9 in D8,E8 because of 5,9 in row F. Thus, both 5,9 are blocked elsewhere in column 8. The 5 at C1 blocks all of row C, so phantom 5’s must exist at either A7 or A9, blocking row A elsewhere.

H6 5 (5's blocked by A?,C1,I3) Where can 5 go in column 6 ?? Only at H6. A? means the phantom 5 in either A7 or A9.

G7 5 (H6,I3)

A9 5 (A7 blocked by G7) Either A7 or A9 must be a 5, so G7 forces 5 at A9.

G4 1 (what's left in row G)

A5 1 (B9,C2,G4,E6)

H5 2 (I8) 2 in I8 blocks bottom row, forcing 2 at H5.

C9 2 (D7,I8)

I7 1 (B9,F8)

I6 3 (D5) 3 in D5 forces 3 at I6.

I5 9 (what's left in box)

I2 7 (what's left in row I)

H2 9 (what's left in box)

E5 5 (phan 5/9 pair in D4,E5) 9 in I5 eliminates the possibility of E5 being a 9, so it must be 5.

D4 9 (what's left in box)

D8 5 (what's left in row D)

E8 9 (what's left in row E)

B4 5 (A9,C1,E5,H6)

A4 7 (what's left in col 4)

B5 4 (what's left in col 5)

A6 2 (B2,C9)

C6 9 (what's left in box)

B3 7 (phan 4/7 pair in B3,C3) 4 in B5 blocks 4 in B3, so B3 must be 7.

C3 4 (what's left in col 3)

A7 9 (C6,E8,G9)

B1 9 (A7)

A1 3 (what's left in box)

A8 4 (what's left in row A)

B8 3 (what's left in row B)

C7 7 (what's left in box)

F7 3 (phan 3/7 in row F) C7 is 7, so F7 can NOT be 7 of the 3/7 pair. So, F7 must be 3.

F9 7 (what's left in box)

(row H completed by columns) A8,D9 give H7=4; C7,F9 give H8=7; B8,F7 give H9=3. Puzzles Solved.