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![[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("1",(5,85)); label("7",(15,85)); label("2",(25,85)); label("3",(35,85)); label("5",(45,85)); label("8",(55,85)); label("4",(65,85)); label("9",(75,85)); label("6",(85,85)); label("4",(5,75)); label("3",(15,75)); label("5",(25,75)); label("9",(35,75)); label("7",(45,75)); label("6",(55,75)); label("1",(65,75)); label("2",(75,75)); label("8",(85,75)); label("6",(5,65)); label("8",(15,65)); label("9",(25,65)); label("4",(35,65)); label("1",(45,65)); label("2",(55,65)); label("7",(65,65)); label("3",(75,65)); label("5",(85,65)); label("9",(5,55)); label("6",(15,55)); label("4",(25,55)); label("1",(35,55)); label("8",(45,55)); label("7",(55,55)); label("3",(65,55)); label("5",(75,55)); label("2",(85,55)); label("5",(5,45)); label("1",(15,45)); label("3",(25,45)); label("2",(35,45)); label("6",(45,45)); label("4",(55,45)); label("8",(65,45)); label("7",(75,45)); label("9",(85,45)); label("7",(5,35)); label("2",(15,35)); label("8",(25,35)); label("5",(35,35)); label("3",(45,35)); label("9",(55,35)); label("6",(65,35)); label("1",(75,35)); label("4",(85,35)); label("8",(5,25)); label("5",(15,25)); label("6",(25,25)); label("7",(35,25)); label("2",(45,25)); label("1",(55,25)); label("9",(65,25)); label("4",(75,25)); label("3",(85,25)); label("3",(5,15)); label("4",(15,15)); label("7",(25,15)); label("6",(35,15)); label("9",(45,15)); label("5",(55,15)); label("2",(65,15)); label("8",(75,15)); label("1",(85,15)); label("2",(5,5)); label("9",(15,5)); label("1",(25,5)); label("8",(35,5)); label("4",(45,5)); label("3",(55,5)); label("5",(65,5)); label("6",(75,5)); label("7",(85,5)); [/asy]](http://latex.artofproblemsolving.com/a/5/c/a5c1e2de1a8ae27672e0b4ebd7ed6eaca7314d66.png)
![\[w+x+y+z = \boxed{22}\]](http://latex.artofproblemsolving.com/f/f/5/ff5ad8a2a826a251c569018bba02ead8633b1aac.png)
