Thursday, 13 August 2009
12-08-09
給自己訓練一下數學吧~
有空的話讓我做個數學100問 O_O~
Algebra, Ineq., Combinatorics, Number theorey, Geometry
各出20題然後自己解……
NT(number theorey) Q1.
(n,m) denote G.C.D. of m,n.
Prove (m,n)/n * nCm is an integer.
solution
lemma : for (m,n)=d, exists +ve integer a,b such that am+bn=d.
(m,n)/n * nCm = (am+bn)/n * nCm = am/n * nCm + bn/n * nCm = a(n-1)C(m-1) + bnCm.
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唉~上完呢堂IMO training真係#^%(#
佢講Extended Binomial Theorem講到我聽聽下將以前係pure maths學D Binomial thm忘記晒!!
Extended Binomial Theorem: (1+x)^n = 1 + nx + (n r) x^2 + ...
where (n r) = [n(n-1)(n-2)...(n-r+1)/r!] for all reals.
Examples : How many natrual numbers, less than 100000, have their digit sum equal to 17?
Solution: <=> (1+x+x^2+...x^9) ^5, the coeff. of x^17.
<=> (1-x^10)^5(1-x)^-5 =..... => 4435.
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升到#6了
29 hours agowmfchris has risen 1 rank, now placed #6 overall (Taiko).
30 hours agowmfchris has risen 1 rank, now placed #7 overall (Taiko).
30 hours agowmfchris has risen 1 rank, now placed #8 overall (Taiko).
35 hours agowmfchris has lost first place on Home Made Kazoku - Shonen Heart [Hard] (Taiko)
36 hours agowmfchris has risen 20 ranks, now placed #657 overall (CatchTheBeat).
36 hours agowmfchris has risen 2 ranks, now placed #7 overall (Taiko).
36 hours agowmfchris has risen 1 rank, now placed #9 overall (Taiko).
保持著"不失#1超過24小時"紀錄。
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我大概被楠和紫欣痛毆N次了~ 拖稿那麼久……不過我還是15/8以後才有空啊。
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