94 Λυμένες Ασκήσεις ΑΕΠΠ

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94 Λυμένες Ασκήσεις ΑΕΠΠ

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94 ()
....( ' )version 0.1 2014

. , . . . . . . . , , , . . . . ( ) ( ) . . , . . , . . , . . , , . . . ' , . . . , . . , ( ). . . . project Euler dzone.com Thursday code puzzler. . , . , ( ). , ., , ( ). . . ( ). . . 1/3 ' . 1/3 , . , 1/3 . , , . 1/3 ' . . . . . ( ). . , , , , . 17 . , , . . , . , . . . , , . . , , . , , , , :[email protected]

1 1 - 1 21 3 - 1 4 - 2 5 - 2 6 - 1003 3 7 - 3 8 - /4 9 - 4 10 - (1)5 11 - (2)6 12 - 7 13 - & 7 14 - 8 15 - 8 16 - 9 17 - 9 18 - 29 19 - 10 10 20 - 10 21 - / 11 22 - 11 23 - Collatz11 24 - Fibonacci13 25 - 14 26 - Horner15 27 - ( _)16 28 - 17 29 - 17 30 - / 18 31 - 18 32 - 19 33 - _19 34 - 20 35 - ( )21* 36 - 21 37 - 2324 38 - 24 39 - 24 40 - 24 41 - 25 42 - 25 43 - 26 44 - 26 45 - 27 46 - / 28 47 - ( )28 48 - 29 49 - 30 50 - 31 51 - 32 52 - /32 ( ) 33 5333 54 - 34 55 - 34 56 - 34 57 - 35 58 - 35 59 - 36 60 - ( )36 36 61 - ( )36 62 - ' 37 63 - 38 64 - 39 65 - ( )41 66 - 43 67 - 44 68 - 45 69 - 24 1246 70 - 47 71 - 1 n47 72 - 48 73 - ( )49 - 50 74 - 50 7551 76 - 3 52 77 - 52 78 - - 53* 79 - - 53 80 - ;54 81 - ( )56 82 - 57 83 - ' ( )58 84 - 59** 85 - - ( )60 86 - 64 87 - 64* 88 - ( )65 89 - 66 90 - -67* 91 - -68 92 - 69 93 - 69 94 - 70

1 - " "

< 0 (-1)*

" : ", 2 . 35 20 . 20% . 11% . , . // , // ! 35 + *20 +

! * 0.2 - * 0.11

! - -

" : ", " : ", + " : ",

3 - , . . . " 1 () " " 2 () "

! ! !

" = ", " = ", 4 - . 3 . ( ) . : 125.25 41, 56.23 18, 2.5 0. " ? "

_ _() _ div 3! _() div 3 !

" ", 5 - , , . 20% 5% . : 56, 12 9 , : = 772,8 , = 38,64 , = 734,16 " ? " " ? " " () ; "

( + *0.2) * ! * + *0.2* (**)

0.05* -

" : ", " : ", " : ", 6 - 100 . : 15732 15700 , 15784 15800 , 60 100 , 530 500 , 17 0. 100 " : "

+ 50 ! 50 / 100 ! 2 _() ! *100 !

! _( ( + 50)/100 ) * 100 ! 7 - . , " () : " " x () : " " () : "

^2 -4** !

= 0 " "_ < 0 " " "1 = ", (- + _()) / (2*) "2 = ", (- - _()) / (2*)_ 8 - / . . () . , . ! ' ..! ..

" 1 : " !

" 2 : " < ! ' " 3 : " < ! '

" ", 9 - . . : . , 20 .

20 .

, 5 .

, , , 1 .

, . . . " (/): " = '' ! ''

" (/): " = ''

0 0 5 5 _ 20 _ 20 1 1 _

" ", , " " " ", , " " . . . , ( 14 ). ( 66). . 10 - (1) . . _ " 1 : " " 2 : "

mod 2 = 0 mod 2 = 0 " " " "_ mod 2 = 0 " " " "_ _

. " 1 : " " 2 : "

__1 mod 2 = 0__2 mod 2 = 0

__1 __2 " "_ __1 __2 " " " "_ 11 - (2) 2_2006 x x mod 2 = 0 y x div 2 y 10 y 2*x + y_y x^2_ y . ( 2006) 2_2006 x

x x mod 2 = 0 x x 20 ! , - 20y x div 2 + 2*x _ x ! , 20 y x div 2 ! , y x^2 _ y -_ ! ( ). _ . _ . x x20 x. , 20. , ( 33). x, . , ( 45). 12 - , . . " x : " " : "

= 0 = 0 " ( x )" _ = 0 0 " ( )" " : ", -/ _ 13 - & (..) () , . , 1% , 1 3, . . " : "

* 0.01

< 1 1 _ > 3 3 _

" : ", 14 - : 20 600 . 600 0.20 5 ( ). 23%. ( ) . " () : "

20 !

> 60 - 600 ! div 5 ! 5 ! , ..! .. mod 5 0 + 1 ! 5

+ * 0.2 _

* 1.23 !

" : ", 15 - , 2.5% , 118. . " : "

* 0.025 > 118 118 -

" : ", 16 - 50 10 25 . , 10 , 30 . . . : : " : " _ 0

[2] [1], " 1 " _

! 2 - 1 [] > [ - 1] [] > [ + 1] [], " ", , " " _ _

! [] > [ - 1] [], " ", , " " _. . . 48 - 20 . ( ). () () ; ( )() , . ( ). . : , : , : , 5000) ...... ( > 10000 12** > 10^8) 54 - ( Excel), , ( ). . , . 32,451 32,45, 2312,017 2312,02 0,996 1,00. :(i) 2 ( 100)(ii) 0,5 (iii) ( _())(iv) ( 100) _( (*100) + 0.5 ) / 100 55 - , , . , ==. ; = = 56 - . . . , . , . . ( ) ....( ) 1: ( ). . 2: , ( ) .... ( ) . . ( ), . . 57 - . , . 24 , 0 23. 8 21, . , . . 8 21, . ( >= 8 1900 < 2100 > 0 < 13 > 0 ( 0 , " ", [i] mod [i] ! __

. :i 0 i < 10 > 0 i i + 1 div [i] > 0 , " ", [i] mod [i]__ 62 - ' : 2, 5, 7, 8, 10, 12, ...( )..., 100. , . 1 100 = 2 = 5 = 7 ( 8 mod 2 = 0) _ _ 1 5 . : 2 5 7 8 100 _ 2 _ 63 - 30 , . 30 0,02 0,03 . . . . ():

:
:

! , 30*0.02=0.6
30 ! ,
! [] _ _ , . ( ) . . . . ' .** 85 - - ( ) [] - . . - . - ( , ). =10 =5. . . 5 . . , . . .! () : [5], 1 5 []