Олимпиадные задания по информатике

8 – nji synp I – tur .

1 . Sifrleriniň iki essesiniň jemi sifrleriniň köpeltmek hasylyna deň bolan ikibelgili

sanlary yzygider çap etmeli .

Meselem 36 = ( 2*( 3 + 6 ) = 3 * 6 ) , 44 = ( 2 * ( 4 + 4 ) = 4 * 4 )

2 . Berlen n – sandan geçmeýän düzme sanlaryň jemini tapmaly .

Meselem : n = 10 bolsa , onda jogap 37 – e bolmaly .

3 . Berlen tekstde berlen harp bilen başlanýan sözleriň sanyny tapmaly .

Meselem : Berlen tekst “ Alma biş , agzyma düş “ we berlen harp “ a “

bolsa , onda jogap 2 – i bolmaly .

4 . Sagat , minut , sekunt berlen . 1 – sekunt mundan öňki wagty kesgitlemeli .

5 . a( n , n ) kwadrat matrisanyň gapdal diagonaldan ýokarda ýerleşen

elementleriniň içinden täkleriniň jenini tapmaly .

Meselem : n = 3 we matrisa bolsa jogap 25 bolmaly.

8 – nji synp II – tur .

1 . Koordinata tekizliginde berlen X(n) we Y(n) koordinataly nokatlaryň

tekizlikdäki şekiliň her bir çärýegine näçe sanysy degişli .

2 . Töwerek boýunça sagat strelkasynyň garşysyna hereket edýän nokadyň

maksatnamasyny ýazmaly .

3 . 1 – den ( 2n – 1 ) – e çenli sanlary a( n , n ) matrisada setirler we sütünler

boýunça artar ýaly gurnamaly .

Meselem : n = 3 bolsa , onda jogap bolmaly .

Ýumuşlaryň çözüwleri 8 – nji synp I – tur .

1 . for i = 1 to 9 : for j = 0 to 9

if 2*( i + j ) = i * j then ? 10*i + j

next j : next i : stop ; end .

2 . input n : for i = 1 to n : k = 0 : S = 0 : for j = 0 to i

if i mod j = 0 then k = k +1 : next j

if k 2 then S = S + i : next i : ? “ S = “ ; S : stop : end .

3 . input a$ , rb$ , rs$ : a$ = a$ + “ “ : S = 0

for i = 2 to len(a$) : x$ = mid$( a$ , i – 1 , 1 ) : y$ = mid$( a$ , i , 1 )

if ( x$ = rb$ or x$ = rs$ ) and y$ = “ “ then S = S + 1 : next i

? “ S = “ ; S : stop : end .

4 . input s , m , c : a$ = “ 1 – sekuntdan soňky wagt “ : c = c – 1

if c

s = s +1 : if s

5 . input n : dim a ( n , n ) : S = 0

for i = 1 to n : for j = 1 to n : input a ( i , j ) : next j : next i

for i = 1 to n : for j = 1 to n : ? using “###” a ( i , j ) : next j : next i

for i = 1 to n : for j = 1 to n : if i + j = n + 1 : and a( i , j ) mod 2 = 1

then S = S + a( i, j ) : next j : next i : ? “ S = “ ; S : stop : end .

8 – nji synp II – tur .

1 . input n , k : dim X ( n ) , Y ( n ) : for i = 1 to n : input X(i) , Y(i) :

next i : a$ = “ tekizlikdäki şekiliň “ : b$ = “ – çärýegine degişli nokatlaryň sany= “

t1 = 0 : t2 = 0 : t3 = 0 : t4 = 0 : for i = 1 to n

if x 0 and y 0 and abs( x ) + abs( y )

if x 0 and y 0 and abs( x ) + abs( y )

if x 0 and y 0 and abs( x ) + abs( y )

if x 0 and y 0 and abs( x ) + abs( y )

next i : ? a$ ; I ; b$ ; t1 : ? a$ ; II ; b$ ; t2 : ? a$ ; III ; b$ ; t1

? a$ ; IV ; b$ ; t4 : stop : end .

2 . input x1 , y1 , r : pi = 3 . 14 : color 1 , 15 , 3 : screen 12

for i = 0 to 2*pi step 0.4 : x1 = x1 + r*Cos( i ) : y1 = y1 + r*Sin ( i )

pset ( x , y ) , 3 : for i = 1 to 500 : next i : pset ( x , y ) , 15 : next i : 5 goto 5

3 . input n : dim a ( n , n ) :

for i = 1 to n : for j = 1 to n : input a ( i , j ) : next j : next i

for i = 1 to n : for j = 1 to n : a ( i , j ) = i + j - 1 : next j : next i

for i = 1 to n : for j = 1 to n : ? using “###” ; a ( i , j ) : next j : next i

stop : end .

9 – njy synp I – tur .

1 . Berlen n sandan geçmeýän täk düzme sanlaryň jemini ikilik ulgamda çap

etmeli . ( Meselem : n =25 bolsa , jogap 1000110 bolmaly )

2 . Ilkinji iki fifriniň kwadraty bilen soňky sifriniň kwadratynyň tapawudyna deň

bolan üçbelgili sanlary yzygider çap etmeli .

(Meselem : 100 =(10^2 – 0^2) ; 147 =( 14^2 – 7^2 )

3 . Tekstdäki boşluklary ( probel) aýyryp testi gysmaly .

Meselem : AAA BBB DDD bolsa , AAABBBDDD bolmaly

4 . 2009 – njy ýylyň ilkinji dynç güni ýanwar aýynyň 4 – i bilen gabat gelýär .

2009 – 2099 – njy ýyllar aralygynda näçä sany dynç gýni bar ?

5 . a(n , n ) kwadrat matrisa berlen . Onuň çyzgydaky “ ? “ – belgi goýulan

bölegindäki iň uly elementini çap etmeli .

9 – njy synp I I – tur .

1 . Koordinata tekizliginde berlen x(n) , y(n) nokatlaryň umumy merkezi

koordinata başlangyjynda bolan r1 we r2 ( r1

halkanyň herir çärýegine näçe sanysy dýşýär ?

2 . n – sany m – belgili san berlen . Bu sanlaryň içinden jübütleriniň täk

sifrleriniň jemini tapmaly .

Meselem : n = 4 , m = 4 we a1 = 3847 , a2 = 2754 , a3 = 4171 , a4 = 1762 bolsa , onda bu sanlaryň jübütleri a2 we a4 olaryň täk sifrleriniň jemi

S = 7 + 5 + 1 + 7 = 20 , ýagny jogap 20 bolar .

3 . Ekranda grafiki görnüşde a(x1 , y1) , b(x2 , y2) nokatlar berlen .Gozganmýan

a – nokadyň daşyndan ab – kesimi sagat peýkamynyň garşysyna hereketlendirmeli

4 . Berlen tekstde berlen harp bilen başlanýan we berlen harp bilen gutarýan sözleri

çap etmeli .

Ýumuşlaryň çözüwleri 9 – njy synp I – tur .

1 . input n : for i = 1 to n : k = 0 : S = 0 : for j = 1 to i

if i mod j = 0 then k = k + 1 ; next j

if k 2 and i mod 2 = 1 then S = S + 1 : next i : d$ = “ “

5 k = s \ 2 : m = 2*( s / 2 – k ) : d$ = str$( m ) + d$ : b = k

if b = 2 then 5 : d$ = str$( b ) + d$ : ? d$ : stop : end .

2 . for i = 1 to 9 : for j = 0 to 9 : for k = 0 to 9

if ( 10*i + j )^2 – k^2 = 100*i + 10*j + k then ? 100*i + 10*j + k

next k : hext j : next i : stop : end .

3 . input a$ : x$ = “ “ : n1 = 1 : 5 n = instr ( n1 , a$ , x$ ) : if n = 0 then 10

if n = 1 then a$ = right$( a$ , len(a$) – 1) : goto 10

if n = len(a$) then left$(a$ , len(a$) – 1 ) : goto 10

a$ = left$(a$ , n – 1) + right$(a$ , len(a$) – len(x$) – n + 1) : n1 = n + 1 : goto 5

1. ? a$ : stop : end .

4 . a$ = “ 2009 – 2099 – njy ýyllarda “ : b$ = “ – sany dynç güni bar “ : n = 0

for i = 2009 to 2099 : if i mod 4 = 0 then g =366 else g = 365 : n = n + g

next i : k = 0 : for j = 4 to n : j = j – 4 : j mod 7 = 0 then k = k + 1 :

next i : ? a$ ; k ; b$ : stop : end .

5 . input n : dim a( n , n )

for i = 1 to n : for j = 1 to n : input a ( i , j ) : next j : next i

for i = 1 to n : for j = 1 to n : ? using “###” a ( i , j ) : next j : ? : next i

max = a (1 , 2) : for i = 1 to n : for j = 1 to n

if i max then max = a(i , j )

next j : next i : ? “ max = “ ; max : stop : end .

9 – njy synp II – tur .

1 . input n , r1 , r2 ( r1 : dim X ( n ) , Y ( n ) : for i = 1 to n : input X(i) , Y(i)

next i : a$ = “ tekizlikdäki şekiliň “ : b$ = “ – çärýegine degişli nokatlaryň sany = “

t1 = 0 : t2 = 0 : t3 = 0 : t4 = 0 : for i = 1 to n

if x 0 and y 0 and x^2+y^2= r1 and x^2+y^2

if x 0 and y 0 and x^2+y^2= r1 and x^2+y^2

if x 0 and y 0 and x^2+y^2= r1 and x^2+y^2

if x 0 and y 0 and x^2+y^2= r1 and x^2+y^2

next i : ? a$ ; I ; b$ ; t1 : ? a$ ; II ; b$ ; t2 : ? a$ ; III ; b$ ; t1

? a$ ; IV ; b$ ; t4 : stop : end .

2 . input n , m : dim a(n) : for i = 1 to n ; input a( i ) : next i

for i = 1 to n ; ? a( i ) : next i : for i = 1 to n x$ = str$(a( i)) : for j = 1 to m

k = VAL(mid$(x$ , j , 1 )) : if a(i)mod2=0 and k mod 2=1 then S = S + a(i) : next j

? “ S = “ ; S : stop : end .

3 . input x1 , y1 , x2 , y2 : pi = 3 . 14 : r = sqr((x2-x1)^2+(y2-y1)^2) : color 1 , 15 , 3

Screen 12 : for i = 0 to 2*pi step 0.4 : x = x2 +r*cos(i) : y = y2 + r*sin(i)

line (x1,y1) – (x,y) , 3 : for j=1 to 500 : next j : line (x1,y1) – (x,y) , 15 : next i

4 . input n , rb$ , rs$ : dim a$(n) : for i = 1 to n ; input a$( i ) : next i

for i = 1 to n ; ? a$( i ) : next i : for i = 1 to n b1$ = left$(a$(i) , 1 )

b2$ = right$(a$(i) , 1 ) : if ( b1$ = rb$ or b2$ = rs$ ) and ( b2$ =rb$ or b2$ = rs$ )

then ? a$(i) ; “ “ ; next i : stop : end .

10 – njy synp I – tur .

1 . Berlen n – sandan geçmeýän täk düzme sanlaryň içinden polindrom

bolýanlarynyň ikilik ulgamdaky ýazgysynyň hem polindrom bolýanlaryny

yzygider çap etmeli . Meselem : n = 35 bolsa , jogap 33 ; 100001 bolmaly .

2 . Sifrleriniň kublarynyň jemi bu sanyň özüniň kwadratyna deň bolan ikibelgili

sanlary yzygider çap etmeli Meselem : 27 ; 2^3 + 7^3 = 27^2 .

3 . Berlen tekstdäki “ ! “ – belgileri “ ? “ – belgi bilen çalyşmaly .

4 . Berlen n – san boýunça ( n

5 . Ekranda töwerek gurmaly . “ u “ – harpy basylanda töwerek ulalmaly ,

“ k “ – harpy basylanda bolsa kiçelmeli .

10 – njy synp I I – tur .

1 . Koordinata tekizligimde berlen x(n) we y(n) koordinataly nokatlaryň

tekizlikdäki şekiliň her bir çärýegine näçe sanysy degişli .

2 . Ikilik ulgamda berlen sany onluk ulgama geçmeli .

Meselem : 101 . 11 berlen bolsa jogap 5 . 75 bolmaly .

3 . 1 – den n^2 – a çenli sanlary 1 – nji setirde 1 – den n – e çenli artar ýaly ,

ikiji setirde 2n – den n + 1 – e çenli kemeler ýaly , üçünji setir 2n + 1 – den

3n – e çenili artar ýaly we şeýle gezekleşip täk setirler artyp we jübüt setirler

kemeler ýaly gurnamaly .

Meselem : n = 4 bolsa , onda a(n,n) = bolmaly .

4 . 2n – tertipli a( 2n , 2n ) kwadrat matrisa berlen . Onuň n*n bloklarynyň

ornyny aşakdaky ýaly çalyşmaly .

Meselem n = 2 we a(n,n)= bolsa onda a(n,n)= bolmaly .

Ýumuşlaryň çözüwleri 10 – njy synp I – tur .

1 . input n : dim a(n) : t = 0 : for i = 1 to n : k = 0 : for j = 1 to i : if i mod j = 0

then k = k + 1 : next j : if k 2 and i mod 2 = 1 then t = t + 1 : a(t) = i ; next i

for i = 1 to t : x$ = str$(a(i)) : y$ = “ “ : for j = 1 to len(x$)

y$ = mid$(x$,j,1) + y$ : next j : if x$ y$ then 10 : a = VAL ( x$ ) : d1$ = “ “

5 . k = a \ 2 : m = 2*(a / 2 – k ) : d$ = str$( m ) + d1$ : a = k : if a 2 then 5

d1$ = str$( a ) + d1$ : d2$ = “ “ : for j = 1 to len(d1$) : d2$ = mid$(d1$ , j , 1) + d2$ :

next j : if d1$ = d2$ then ? a(i)$ ; “ “ ; d1$ ; 10 next i : stop : end .

2 . for i = 1 to 9 : for j = 0 to 9 : if i^3 + j^3 = ( 10*i + j )^2 then 10*i + j next j , i

3 . input a$ : b1$ = “ ! “ : b2$ = “ ? “ : n1 = 1 : 5 n = instr( n1 , a$ , b1$ ) :

if n = 0 then 10 : if n = 1 then a$ = b2$ + right$( a$ , len( a$ ) – 1 ) : goto 10

if n = len ( a$ ) then a$ = left$ ( a$ , len ( a$ ) – 1 ) + b2$ : goto 10

a$ = left$ ( a$ , n – 1 ) + b2$ + right$ ( a$ , len ( a$ ) – n + 1 ) : n1 = n + 1 : goto 5

10 ? a$ ; : stop : end .

4 . dim a(12) : for i = 1 to 12 : read a ( i ) : next i

data 31 , 28 , 31 , 30 , 31 , 30 , 31 , 31 , 30 , 31 , 30 , 31 : 5 input n : if n 365 then 5

for i = 1 to n : if n

5 . x = 320 : y = 240 : r = 50 : color 1 , 15 , 3 : screen 12 : 5 inkey$ : circle ( x , y ) , r , 3

if a$ = “ U “ or a$ = “ u “ then r = r + 10 : if a$ = “ K “ or a$ = “ k “ then r = r – 10

if a$ = chr ( 27 ) then stop : goto 5 .

10 – njy synp II – tur .

1 . input n , r , k : dim X ( n ) , Y ( n ) : for i = 1 to n : input X(i) , Y(i) next i

a$ = “ tekizlikdäki şekiliň “ : b$ = “ – çärýegine degişli nokatlaryňsany = “

t1 = 0 : t2 = 0 : t3 = 0 : t4 = 0 : for i = 1 to n

if x 0 and y 0 and x^2+y^2= r and abs( x ) + abs( y )

if x 0 and y 0 and x^2+y^2= r and abs( x ) + abs( y )

if x 0 and y 0 and x^2+y^2= r and abs( x ) + abs( y )

if x 0 and y 0 and x^2+y^2= r and abs( x ) + abs( y )

next i : ? a$ ; I ; b$ ; t1 : ? a$ ; II ; b$ ; t2 : ? a$ ; III ; b$ ; t1

? a$ ; IV ; b$ ; t4 : stop : end .

2 . input a : b = fix ( a ) : c = a – b : x$ = str$( b ) : y$ = str$( c )

rem . Sanyň bitin bölegi ikilik ulgama geçilýär . s1 = 0 : n = len ( x$ ) : for i = 1 to n

m = VAL( mid$( x$ , i , 1 ) : s1 = s1 + m*2^( n – 1 ) : next i : q1$ = str$ ( s1 )

rem . Sanyň drob bölegi ikilik ulgama geçilýär . s2 = 0 : n = len ( y$ ) : for i = 1 to n

m = VAL( mid$( y$ , i , 1 ) : s2 = s2 + m*( 1 / 2 )^i : next i : q1$ = str$ ( s1 )

q$ = q1$ + “ . “ + q2$ : ? q$ : stop : end .

3 . input n : dim a ( n , n )

for i = 1 to n : for j = 1 to n : if i mod j = 1 then a ( i , j ) = ( i – 1 ) * n + j

else a ( i , j ) = i * n + 1 – j : next j : next i

for i = 1 to n : for j = 1 to n : ? using “###” a ( i , j ) : next j : ? : next i

4 . input n : dim a ( 2n , 2n )

for i = 1 to 2n : for j = 1 to 2n : input a ( i , j ) : next j : next i

for i = 1 to 2n : for j = 1 to 2n : ? using “###” a ( i , j ) : next j : ? : next i

for i = 1 to n : for j = 1 to n : p = a ( i , j ) : a ( i , j ) = a ( n + i , j )

a ( n + i , j ) = a ( n + i , n + j ) : a ( n + i , n + j ) = a ( i , n + j ) : a ( i , n + j ) = p : next j , i

for i = 1 to 2n : for j = 1 to 2n : ? using “###” a ( i , j ) : next j : ? : next i

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