+ + 4 + + 998999 + 999000 + 4 + + 4 + 40 + 60 + 84 + + + 6 + 99 + 4 994 994994 9999

= +

4

abcd

9 7 7

7 4 4 4 6 4

9 4 4

4 7 7 90 0 8

8 40

n + n + n

00 70 0 0 70 0 0 40 0 60 40 0 4 60 0 0 90 0 0 6 90 0 0 7 0 70 0 8 0 0 0 9 0 0 0

= 4 4 4 7 4 9 6 = + 4 4 4 7 4 + 4 9 4 6 n = 4 4 4 + 4 4 4 + 44 n 4-4 4 4 + 4 n 4 4-4 n

> 0 0 0 0 < 0 < < < + + 4 + Λ Λ + + 998 999 999 000 =, =, 4 =, 4

Λ Λ = 999 000 999 0000 = - + + + Λ Λ + + 4 998 999 999 000 999 = = 000 `000 + + + + + + 4 4 40 60 84 + + + + + 6 99 4

= ( - ) + ( - 4 ) + ( 4-6 ) + ( 6-8 ) + ( 8-0 ) + ( 0 - ) + ( - 4 ) = - + - 4 + 4-6 + 6-8 + 8-0 + 0 - + - = - 4 = 4 = ( - ) + ( + ) + ( ) + ( ) + ( + ) + ( 7 7 9 9 ) = + + 7 + 7 9 + 9 + = = 994 994 994 99 99 994 994994 9900 994 = 994 ( 994 + ) ( 994 ) 994 = 994 ( 994 ) 994 = 994 994 994 + = 4

= = 6 = = 4 4 0 4 = = 7 7 9 = = 4 7 4 7 8 =

= 4 = 4 4 = + 4 BC = BD ABD = ABC AC = 4EC DEC = ADC = 4 ABC 4 4 = ABC ADG = ADE = ABC FGE = ABC

FGE ABC = 0 = + ( ) = + = 6

% 4 % = 00 4 4 00 = 00 = %

A () () () B (4) C ()() (4) () () D () (6) () (6) E (6) ()(6)

abc

abcd abcd 000a 00b + Oc d

990 0 0 + = 0( 0 ( 0 + 990) 0 = 660 ( 00 + 999) 999-00 + = 900 = 4940

7 9 7 7 9 7 408 9 7 6 - - 9-7 = 4 7

6 7

7 4 4 4 7 = 4 = 4 4 6 4 (- 6 ) 6 = - = - 6 4 6 4 6 = (- 4 6 6 6 ) = 6 6 6 6 = 8 6

- = 6 6 6 = - 6 = 8 6 = 8 8 6 6

4 0 + = 4 0 0 0 = 0 0

+ = + = 7 7 + = 4 4 + + 4 6 + + = 60( ) 4

+ - - ( - ) = 6 = 6

7 8 8 0 0

60 60 = 60 70 40 = = = 4 7 ( ) 8 8 4 7

9 6 4 9 4 - = 9 4 6 - - = 6 6 - = 9 4 6 - = 6 6 = =

= = 8 = 8 8 9 = 6 8 + 9 = 8 + - = 4 = ( ) 8 4 4 ( 4 ) = = 4 8 4 [ - 4 - ] 8 = [ - ] 4 = 4 = 4 - = 8 4

4 8 8= 8 0 8 = 9-9 = 0 0 4 0 0 0 0 [ - 8 8] 8 4 = [ 4-9 0 ] 0 = 0 0 = 6 6 = 4 4 = 6 ( 6 ) ( ) 4 4 ( ) = 6 = 6 = ( )

( + + ) 0 0 ( + + 0 0 ) = 0 + = 0 0 4 = + 4 = + 4 = 7

0 44 = 90 0 + + 44 = 0 + + 44 = 89 0 + + 90 4 0 7 7 4 4 0 7 7 4 00 7 4 00 = 00 7

900 00 00 900 = 4 4 00 900 900 = 60 8 4 8 99.7 8 99 4 99 99 4 99 7 = 9 4 99 4.7 = 9

4 40 = 6 0 = 6 A D 8 60 = 4 6 4 7 =, 7 6 8 4 0 =, = 7 7 8 0 80 7 7 7 80 7 = A 4 40 = 6 0 = 6 8 60 = 4 807 = A

x + 4y + 00 - x - y = 00 7 x = 0-7 0 7 x y 0

6x y z = x 4y z =

4 x + 4 00 - x = 00 4 xy = 6 6x = 8y x = 4 y 4 y y = 6 y4 x = y = 4 x = y - 0 6x = y4 x = 44 y = 40

x -= y x= y - x = y = 40 8 8 x - 40 = 8 x - 40 x -0= 8 8 x - 40 - x = 0-40 8 8 x = 440 x y y =.- 0.- 4 6 6x + 4y + y =

4 6 7 8 9 0 0 9 8 7 6 4 0 4 6 7 8 9 0 0 8 4 8 0 0

7 7 A B x A B 7 B 9 - x = - x x 7 = - x 8

7 x = 6 6 x =. 7 x =

+ + + + + + + + + 6 0 0 4 6 7 90 0 + + + + + + + + 6 0 8 6 4 + + + + + + 4 8 + + Λ Λ + 4 4 7 8 9 0 4 7 4.6 4 9 7 0 4 9 0 8 6 9 7 0 00 6 0 0 4

6

0 0 4 7 9 00 9 8

4 6 8 6 4 0 8 0 4 0 8 6 4 6 8 40 48 46 44 4 98 99 00 4 99 00 0 4 00 0 0 00 0 0 97 98 99 4 6 7 8 9 0 4 6 4 4 4 4 4 4 4 4 4 0

48 9 0

88 4 + 44 + 49 + Λ Λ + 4 00 94 4 0 6 0 4 4 4 ( ) 0 ( ) 9 ( ) ( ) 9 9 60

9 80 40 0 4 99 9 40 00 4 84 98 6 0 7 7 97 7 0 88 8946 90666 9 84 9999099