Bi 1: (Bi ton m) a. C bn cch phn b 52 sinh vin vo 13 nhm thc tp,
mi nhm c 4 ngi nu cc nhm ko dc nh s. b. C bn cch sp xp 60 vin bi
thnh dy gm 10 bi , 20 xanh, 30 trng? c. C bn xu nh phn di 10 hoc
cha 5 s 1 lin tip hoc cha 5 s 0 lin tip. d. Gi An l s lng xu nh phn
di n ko cha 110 nh l xu con. Xy dng cng thc quy cho An. Gii CTQ a
ra CT di dng hin cho An e. Gii CT quy: f(1) = 7; f(k+1) = f(k) + 2k
+ 3, k >= 1; f. Tnh s lng nghim nguyn ca PT x1 + x2 + x3 = 20
tha mn 0 =< x1, x2, x3 =< 9 Bi 2: (Bi ton tn ti) Hy cho bit
trong s cc khng nh sau, khng nh no ng, k no sai. Nu ng hy cm, nu
sai hy a ra phn v d a. Trong s 27 s nguyn dng l phn bit, mi s u nh
hn 100 bao h cng tm dc 2 s c tng = 102 b. Trn mt phng cho n im
(n>=3), trong 2 im bt k cch nhau ko qu 1. Khi c ko qu 3n-6 cp im
cch nhau ng 1 c. Trong s 5 im bt k trong 1 hnh vung kch thc 2x2 lun
tm dc 2 im mh khong cch gia chng ko vt qu cn bc 2 ca 2 Bi 3: (Bi
ton lit k) a. a ra 3 hon v tip theo hon v (1, 2, 3, 5, 8, 7, 6, 4)
trong th t t in b. Cho X = {3, 2, 7, 9, 10} l tp con 5 phn t ca {1,
2, 10}. a ra 3 tp con tip theo X trong th t t in c. V cy lit k li
gii theo thut ton quay lui a ra tt c cc xu gm 4 k t, mi k t dc ly t
tp {a, b} ko cha 2 ch a lin nhau. d. M t thut ton quay lui ko quy
lit k cc tp con m phn t ca tp N = {1, 2, , n} Bi 4: (Bi ton ti u) p
dng thut ton nhnh cn gii bi ton ci ti sau: 9x1 + 5x2 + 7x3 + 2x4
-> max 5x1 + 3x2 + 4x3 + 2x4 =< 22 x1, x2, x3, x4 >=0,
nguyn Qu trnh gii theo thut ton trnh by trn cy li gii
---------------- Automerged ---------------Cch gii bi 1: Cu a, b
mnh b qua, ngh l d, t th post cu c ln xem, cu ny nhiu tranh ci y
:bs49: e. (cu ny kh d ^^) Ta c: f(k+1) = f(k) + 2k + 3 f(k) =
f(k-1) + 2(k-1) + 3 f(k-1) = f(k-2) + 2(k-2) + 3
....................................... f(2) = f(1) + 2.1 + 3 f(1)
= 7 _______________________ f(k+1) = 2(1 + 2 + ... + k) + 3k +7 =
k(k+1) + 3k + 7 = (k+1)^2 + 2(k+1) + 4 ---> f(k) = k^2 + 2k + 4
f. Ngh mi th nh lm nh th ny, ko c cch no khc T________T HiXxX Gi
x1, x2, x3 l x,y,z cho d type nh.
V x + y + z = 20 mh x, y, z =< 9 --> 2 =< x,y,z =< 9
(t cm) Nhn thy vi mi cp x,y th ta s c 1 nghim ca pt (v z = 20 - x
-y) z = 20 - x - y Mh z =< 9 --> x + y >= 11 Vi x = 2
--> y = 9 --> 1 nghim Vi x = 3 --> y thuc [8, 9] --> 2
nghim Vi x = 4 --> y thuc [7,9] --> 3 nghim
.................................................. ........... Vi x
= 8 --> y thuc [3, 9] --> 7 nghim Vi x = 9 --> y thuc [2,
9] --> 8 nghim ==>> S nghim ca pt l 1+2+...+8 = 36 Li gii
ca Huyn Anh: chnh xc th cu 1f theo chun l th ny x1 + x2 + x3 = 20 0
Chc chn phi c 2 s c tng l 102 => dpcm b. V 2 im bt k trong n im
ko cch nhau qu 1 -> cc im cho nm trn hoc trong 1 ng trn ng knh
1. Khong cch gia 2 im = 1 2 im l 2 u ng knh ca trn, v t mi im ch c
th c 1 on thng ni n 1 im khc c di bng 1 (v qua 1 im trn ng trn ch k
dc 1 knh) --> Gi s cp im cch nhau ng 1 l X -> X =< n/2. Ta
phi cm X =< 3n -6 !! Ta c: n/2 =< 3n - 6 n >= 2.4 (t bin i
nh ^^) --> X dpcm (Thanks 2 L Tn & Trai bao v li gii ^^)
Error: cu 2b: cng cha xem l ci va ft hin c nh hng j n bi ko nhg c
spam t cho vui :bs9: Thy l "V 2 im bt k trong n im ko cch nhau qu 1
-> cc im cho nm trn hoc trong 1 ng trn ng knh 1." vn cha hn l
bao c ht cc im.Nh 3 im to thnh tam jc u c cc cnh l 1 ,vn tha mn 2
im bt k cch nhau ko qu 1 m ng trn bao quanh n c ng knh l ~ 1,155 c
L Tn vo xem v th Fix li h ci :bs20: FIX Li gii trn l sai, nhng cng
c tnh tham kho nn li cho anh ch em xem, v ko b mc li nh th ^^
Li gii chnh xc th v bun ng lm ri nn cha ngh ra, chung chung li l
nh sau: Cn chng minh X (s cc cp im c di 1) =< n M n =< 3n - 6
l NG (v n>=3) --> X =< 3n - 6 (pcm)
Bonus cho ci hnh v bng word, 6 im 6 on thng, tt c u bng 1 =))
63
c. Chia hnh vung 2x2 thnh 4 hnh vung nh 1x1. Theo nguyn l
Dirichle, 5 im thuc hnh vung 2x2 -> c t nht 2 im phi cng thuc 1
hnh vung 1x1. Mh trong hnh vung 1x1, khong cch ln nht gia 2 im l cn
2 (ng cho) --> 2 im c k/c =< cn 2 --> dpcm
Bi 3 a. 3 hon v tip (1, 2, 3, 6, 4, 5, (1, 2, 3, 6, 4, 5, (1, 2,
3, 6, 4, 7,
theo hon v (1,2,3,5,8,7,6,4) l: 7, 8) 8, 7) 5, 8)
b. 3 tp con tip theo ca X: {3, 2, 8, 9, 10} {4, 2, 5, 6, 7} {4,
2, 5, 6, 8} TIPS: Nn chuyn bi thnh {2,3,7,9,10}, vit cc tp con ri i
li cho nhm ^^
