Difference between revisions of "2006 iTest Problems/Problem 20"
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| + | ==Problem== | ||
| + | Find the sum of <math>w + x + y + z</math> by solving the Sudoku puzzle below. | ||
| + | |||
| + | _ _ _ '''|''' _ 4 _ '''|''' _ z _ | ||
| + | 1 _ 6 '''|''' _ _ _ '''|''' 7 _ 3 | ||
| + | 5 _ _ '''|''' 9 _ _ '''|''' _ _ 2 | ||
| + | '''---------------------''' | ||
| + | _ 8 3 '''|''' w 2 _ '''|''' 5 _ _ | ||
| + | 2 _ _ '''|''' 5 _ 9 '''|''' _ _ 7 | ||
| + | _ _ 7 '''|''' _ 8 _ '''|''' 9 2 _ | ||
| + | '''---------------------''' | ||
| + | 3 _ _ '''|''' _ _ 1 '''|''' _ _ 6 | ||
| + | 8 _ 9 '''|''' x _ _ '''|''' 3 _ 5 | ||
| + | _ y _ '''|''' _ 3 _ '''|''' _ _ _ | ||
| + | |||
| + | <math>\textbf{(A) }2\qquad | ||
| + | \textbf{(B) }4\qquad | ||
| + | \textbf{(C) }6\qquad | ||
| + | \textbf{(D) }8\qquad | ||
| + | \textbf{(E) }9\qquad | ||
| + | \textbf{(F) }10\qquad | ||
| + | \textbf{(G) }11\qquad | ||
| + | \textbf{(H) }12\qquad | ||
| + | \textbf{(I) }13\qquad | ||
| + | \textbf{(J) }14\qquad | ||
| + | \textbf{(K) }15\qquad | ||
| + | \textbf{(L) }18\qquad</math> | ||
| + | <math>\textbf{(M) }19\qquad | ||
| + | \textbf{(N) }20\qquad | ||
| + | \textbf{(O) }23\qquad | ||
| + | \textbf{(P) }24\qquad | ||
| + | \textbf{(Q) }25\qquad | ||
| + | \textbf{(R) }26\qquad | ||
| + | \textbf{(S) }28\qquad | ||
| + | \textbf{(T) }30\qquad</math> | ||
| + | |||
==Solution== | ==Solution== | ||
Latest revision as of 11:49, 15 January 2020
Problem
Find the sum of 
by solving the Sudoku puzzle below.
_ _ _ | _ 4 _ | _ z _ 1 _ 6 | _ _ _ | 7 _ 3 5 _ _ | 9 _ _ | _ _ 2 --------------------- _ 8 3 | w 2 _ | 5 _ _ 2 _ _ | 5 _ 9 | _ _ 7 _ _ 7 | _ 8 _ | 9 2 _ --------------------- 3 _ _ | _ _ 1 | _ _ 6 8 _ 9 | x _ _ | 3 _ 5 _ y _ | _ 3 _ | _ _ _
Solution
![[asy] unitsize(2.5); draw((0,0)--(0,90)--(90,90)--(90,0)--cycle,linewidth(2)); draw((10,0)--(10,90)); draw((20,0)--(20,90)); draw((30,0)--(30,90),linewidth(2)); draw((40,0)--(40,90)); draw((50,0)--(50,90)); draw((60,0)--(60,90),linewidth(2)); draw((70,0)--(70,90)); draw((80,0)--(80,90)); draw((0,10)--(90,10)); draw((0,20)--(90,20)); draw((0,30)--(90,30),linewidth(2)); draw((0,40)--(90,40)); draw((0,50)--(90,50)); draw((0,60)--(90,60),linewidth(2)); draw((0,70)--(90,70)); draw((0,80)--(90,80)); label("7",(5,85)); label("9",(15,85)); label("2",(25,85)); label("3",(35,85)); label("4",(45,85)); label("6",(55,85)); label("1",(65,85)); label("5",(75,85)); label("8",(85,85)); label("1",(5,75)); label("4",(15,75)); label("6",(25,75)); label("2",(35,75)); label("5",(45,75)); label("8",(55,75)); label("7",(65,75)); label("9",(75,75)); label("3",(85,75)); label("5",(5,65)); label("3",(15,65)); label("8",(25,65)); label("9",(35,65)); label("1",(45,65)); label("7",(55,65)); label("6",(65,65)); label("4",(75,65)); label("2",(85,65)); label("9",(5,55)); label("8",(15,55)); label("3",(25,55)); label("7",(35,55)); label("2",(45,55)); label("4",(55,55)); label("5",(65,55)); label("6",(75,55)); label("1",(85,55)); label("2",(5,45)); label("1",(15,45)); label("4",(25,45)); label("5",(35,45)); label("6",(45,45)); label("9",(55,45)); label("8",(65,45)); label("3",(75,45)); label("7",(85,45)); label("6",(5,35)); label("5",(15,35)); label("7",(25,35)); label("1",(35,35)); label("8",(45,35)); label("3",(55,35)); label("9",(65,35)); label("2",(75,35)); label("4",(85,35)); label("3",(5,25)); label("2",(15,25)); label("5",(25,25)); label("8",(35,25)); label("9",(45,25)); label("1",(55,25)); label("4",(65,25)); label("7",(75,25)); label("6",(85,25)); label("8",(5,15)); label("6",(15,15)); label("9",(25,15)); label("4",(35,15)); label("7",(45,15)); label("2",(55,15)); label("3",(65,15)); label("1",(75,15)); label("5",(85,15)); label("4",(5,5)); label("7",(15,5)); label("1",(25,5)); label("6",(35,5)); label("3",(45,5)); label("5",(55,5)); label("2",(65,5)); label("8",(75,5)); label("9",(85,5)); [/asy]](http://latex.artofproblemsolving.com/d/b/d/dbd8496c21f65e77b3633c3534e9495abd685106.png)
Therefore, ![\[w+x+y+z = 5+7+7+4= \boxed{23}\]](http://latex.artofproblemsolving.com/c/2/d/c2d2161b37fbc2dcf870c0d860ac9c40ce1bef95.png)
See Also
| 2006 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 19 |
Followed by: Problem 21 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • U1 • U2 • U3 • U4 • U5 • U6 • U7 • U8 • U9 • U10 | ||
