MOt hoa sr thidt kdmi thuAt mudn in hinh hoa hai mhu bing crich in miu vlng m6t hinh trdn trung tAm dudng kinh a = 100mm vi in mdu d6 m6t sd hinh trdn nh6 bang nhau sao cho chring phu kin hinh trdn trung
tAm, nhfrng phdn kh6ng giao nhau tao thinh cdc cdnh hoa. C6c ciinh hoa
c6 thd chdm 10n nhau. Lric d6 hinh trdn trung tAm c6 mhu da cam.
Dinh cho ban doc
1) 4 hinh trbn nh6 phAi c6 dudng kinh nh6 nhdt lh bao nhiOu cm (chang
han nhu hinh 1) dd chring phu kin duoc hinh trbn trung tAm ?
2) Ban c6 thd sap xdp 5 hinh trbn nh6 ddu c6 dudng kinh b = 61cm dd
chring phfr kin hinh trdn trung tam ?
GIAI EAp : SANG NGUYEN 16 rnPN nANc sd sAC THANG
Trong bing sd bAc thang kidu 2 (h. 2) (xem THTT sd 309 thdng 312003) ta ki hiOu S (m, n) Id sd
cria 6 6 c6t thrl m (ti trdi sang) vh hdng thrl n (tir trOn xudng). Ki hi0u sd a, b, c trong bing nhu hinh 3. ta c6 c6c h0 thric sau ./ a=S(m,n)=(n_l)2+m E' &ii I A(r)\ 3 I 5 6 7 r Hinh 3 =S(m*I,n+1) = rr2+*-7 = S(m, n) + 2(n-1) (1) ()\ c = S(m+|, n+l) = n2+ m+I = S(m, n) + 2n (3) Dd tim c6ng thrlc tinh cdc ddy sd B(x), C(x), (x), E(x) vdi m6i i ta ddt P,(0) = S(i, 1) =
i-t,2) = Pi(1), Pi(3) = S(i-z,3), ...
(l), (2) c6 Pi@) = S(i-x, x+1) = S(i-x+1, x)
1I I
x-1) = Pi@-l) + 2(x-1). Tidp tuc nhu thd Hinh 2 duoc P;(x) = P;(1) + 2[(x-1) + (x-2) + ... + i]
hay P;(;r) = S(i-1, 2) + x(x-l).
Ddy sO B(x) tmg v6i P1r(1) = S(10, 2) = 11 nOn B(x) = i-x+11 vd lay 10 gid tri
nguyAn fi'tttffig rmg vdi c6.c gi6 tri nguy€n li6n tiep x = 0, 1, 2, ...,9. D6y sd C(x) rlng v6i P n0) = S( 16, 2) = 17 n€n C(,r) = x2-x+17 vd ldy 16 gid tri nguy€n t6'liAn tidp tuong rmg vdi r = 0, 1, 2, ...,15. Tudng tu, ddy sd D(x) = ?_x+41ldy 40 gi6
tri nguy€n fi'tng v6i x = 0, 1,2, ..., 39. (O-le tim ra da thrlc ndy). Ddy sd E(x) = x2-x+33 lliy l7 gi6 tri hct. p s6' itng vdi r = g, lO, ll, ...,25. Quan s6t bing ta cflng tim duoc day sd
F(-r) = *2 - * + 63 ldy 29 gi6 tri hop s6' fing vdi x = 24,25, ..., 52.
Dd tim cOng thric tinh ddy sdA(x) vdi m5i7 d4t Q,Q) = S(1,j), Q/l) = S(2, i+l), ... Tt (1), (3) c6
Qlr) = S(x+l, j+x1 = S(x, 7+;r-1) + ZQ+x-l) = Q,@-l) + ZQ+x-l). Tidp tuc nhu thd duoc Qr{x) = S(1,,t)+x(x+2j *l). Ddys6A(,r)ungvdiS(1,3)=5nOnA(x)=x(x+5)+5vdix=0, 1,2,...Neu
ddi bidn sdc6 thd vi6tA(x) =x(x-l) - | = x2 - x- l'i6ix=3,4,5,....
Ciic ban sau c6ldi giAi t6t duoc nhAn tdng phdm :
l)Traong NgocThdo,264514 Lac Long Quan, P. 10, Q. TAn Binh, Tp. Hd Chi Minh. 2)Trdn HodngTi€it,11A6, THPT Phung HiOp, CAn Tho.
PHI PHI 1 2 3 4 5 6 7 8 9 l0 i1 b C D D(x .s(i- Z l 4 -) 6 1 8 o 10 ii t2 5 6 't 8 9 t0 11 l2 IJ ll 1-5 l0 il t2 t3 t4 l-5 l6 t1 18 l9 20 tl t8 t9 ,n 2l 22 23 Z+ 25 20 20 lo 27 28 a( 30 3l 3Z 33 3,1 3-5 36 37 38 39 40 1t /1 43 +4 l-5 -t6 47 4-\4 5D j} ]Wt n4s1l rblrl {t 4\e t 61r,
fsrrl-f" ui';* rr'u+
l
Le{/E }dr" fY*
CUOC THI
,4q 1*W ?ltcfll,?t,yl,?t 4w( fiRq ?
Cudc' thi Ai thdng minh nhanh trt dci c6 3 Cdu d6'gi(ri thi€u trortg clrfi I fi'An s6'312 (6.2003). Dd t:6 nhfhg ldi gidi ddu riin gtii v'e tiu
,voan. 56'ndy xin gi(ti fuiAtL fi|p 3 cdu d6'drrt 2. Ban r'6 thd gti'i bdt git)i
tilng dtrt hadc cri 2 dot chung I phong bi nhrtng cdn gtii o bm cliin
tt'ittrc ngdt, 31.5.2003. Ngodi phong bi ban ghi rd bdi giri du thi CuOc
thi Ai thdng minh nhanh tri cila Tgp chf T'odn hoc vd Tudi trd. IQl
clrtci c'troc tli sd ddng tr€n s6' 3 l6 ra ngdlt I 5 .10.2003 Cluic cdc ban cd mot ki h0 bd lch vd li tlui.
DOT II
Cnu do 4. UONG THUGi
An, Binh vd Chi thudng di boi vdi nhau. Sau d5 ho cing vio quiin udng trh hoic ch phO. That la li
cti An goi ch phO thi Binh sd goi theo Chi. Ndu Binh goi ch phO thi An s6 goi kh6c Chi. Neu Chi udng trir thi An goi theo Binh. Ban hay tim ngudi lu6n lu6n goi mot thf r') d6 Id thLi gi ?
THUY VU CAu do 5. TRdNG HOA
Ir46t ngudi thm vudn yOu to6n dd trdng 12 cdy hoa vdo 1 bdn hoa
nhu hinh b0n. Anh ta du dinh trdng hoa tidp vdo ci{c bdn hoa hinh trbn sao cho s6 cay hoa o 12 hinh trbn cdn trdng ld cric so khric nhau til I ddn 12 vi sd cAy hoa & m6i hinh trbn bing trung binh cong c&a sd cAy hoa 6 4 hlnh trdn tidp gi6p vdi n6. Ngudi ldm vudn dang lfng tirng chd ban giAi drip girip.
CEHa Ha b6ng xAy r c VAN KHANH u do 6. sAx eoxc
i ngudi A vd B choi trb thay phiOn nhau di6u khidn sring dd bin roi b6ng. Ban ddu c6 10 qua nl,rr nhau nim theo hhng ngang c6ch ddu nhau tren giri d6. Ngudi ta dat s(ng de m6i ldn ban chi
a m6t trong hai trudng hop : hoac dan trfng lhm roi I qua b6ng, hoac dan di i')o gita 2 qui b6ng
oooooo r,d 1)ri roi ca 2 qui. Ai b6n roi quA b5ng cu6i cing ld thang. Ngudi A ban ddu tien d6 ldm roi 2 qua b5ng, cbn lai m6t nh6m 2 qui gdn nhau vb m6t nh6m 6 quA gdn nhau. Ban h6y mdch cho ngudi B c6ch choi
dd chic ch6n thing cudc.