. Trudng hop 1 k chin L:6c nityA2-Pn
2OO7 den ba mau
Dd bAi ddng tr0n THTT sd 356 thdng2.2007 do
so sudt d5 in thidu didu kiOn 6 gii thidt nhu dudi
day. Thinh that xin 16i ban doc.
Diiu kiAn: Sau m6i ldn s6p x€p 2007 ddn ba
miu ndu quay theo chidu kim ddng hd 2007 dbn
quanh tdm m6t g6c a nio d6 v6i 0" < a<36'
thi lai duo. c s1r s6p xdp nhu thd (*).
Ldi gitii. Gqi o,. li g6c nh6 nhdt th6a mdn didu
kiOn (*), ndu 360' = do.t + B va 0' < q, < 36',
r nguy0n vi 0'< F < a,thi g6c p cnngth6a min
(*), do d6 360' = do.t. Goi n li sd dEn nam trong g6c a. thi 2007 = n.t vd $ong n dbn phii c6
ci ba miu. Vi 0" < a < 36" n6n I > 10 mi
2007 = 32.223,suy ra chi c6 th€ n = 3 hodc n = 9
(hinh v6). Ta chuydn viOc x€t sd cdch s6p xdp 2007 dEn ba mhu ve vlec xet so
cacn sap xep
ddy n dEn trong
mdt g6c a,vdi
it nhdt mQr
dEn rnhu Tim
& ddu tr6i.
1) Ndu c6 kh6ng qud ba dEn cirng miu lidn
nhau trong m6t g6c a"th\ n< 3 + 3 + 3 = 9 n6n
chi c6 thd n = 3. L:dLc d6 chi c6 2 cdch li Tim, Lam, D6 vh Tim, D6, Lam.
2) Ndu c6 khOng qu6 bdn dbn cing miu lidn nhau trong m6t g6c a" vd. it nhdt m6t miu c6
hai dEn th\Z + 1 + 1 < n < 4 + 4 + 4 ndnchi c6
thd n = 9. Xby ra ba trudng h9p dudi day tuong trng v6i viQc c6 1 ddn Tim, 2 dEn Tim vi 3 ddn
Tim trong ddy 9 dEn.
A. Vdi 1 dbn Tim 6 ddu tr6i ctra d6y 9 dEn thi cdn 8 vi tri cho ddn mIu Lam vd miu D6.
A1. V6i 4 dEn mhu Lam (4 vi tri cbn lai li dbn
miu D6), thi c6 2 trudng hqp 4 dbn cing
miu liOn tidp. Vay c6 Cf -) = 68 c6ch
s5p xdp.
A2.V6i 3 dEn mlu Lam vh 5 dEn mlu D6 thi c6
41cdch.
V6i 3 ddn miu D6 vi 5 ddn miu Lam thi
c6 4l cdch.
A3. Vdi 2 dbn miu Lam vi 6 dbn miu D6 thi c6
10 c6ch.
YoL 2 dEn miu D6 vi 6 dEn miu Ldm thi c6 10 c6ch.
B. Vdi 2 dBn mlu Tim, trong d6 1 ddn Tim 6 ddu tr6i cira ddy 9 ddn thi cdn 8 vi tri cho
I dbn Tfm vh c6c ddn mlu Lam, miu D6.
81. Vdi 3 ddn miu Lam vd 4 ddn miu D6 thi c6
20 trudng hqp 4 ddn cing miu li€n tidp. VAy c6 8.C? - 20 = 260 (c6ch).
82. Vdi 2 dEn miu Lam vh 5 dbn miu D6 thi c6 120 cdch.
VotZ dbn miu D6 vi 5 dbn miu Lam thi c6120 cdch.
C. Vdi 3 dbn mdu Tfm, trong d6 c6 1 dEn Tfm 6
ddu tr6i ctra ddy 9 ddn thi cbn 8 vi tri cho 2 dEn miu Tim, 3 dbn miu Lam vi 3 dbn miu
D6. V{y c6 Cfr.C} = 560 (c6ch).
Nhu viy tdng sd c6ch s6p x€p 2007 ddn ba miu
trong trudng hgp n = 9 Ld 1490 cdch.
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