[閒聊] 您累了嗎看份考古題吧

看板CSHS57th314作者asdofe (沒有一天到晚在過年的啦)時間16年前 (2009/11/11 17:42)推噓1(1推 0噓 0→)

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這是我讀ds讀到很煩很煩的時候無聊看ntu的考古題版的時候看到的重點是第十一題...XDDD 真是有梗的老師XDDD 十分沒來上課就掰嚕~~~XD 像我就會掰= =" 作者 oscarchichun (ㄍ一) 看板 NTU-Exam 標題 [試題] 98上陳健輝離散數學第一次期中考時間 Wed Oct 28 21:14:03 2009 ─────────────────────────────────────── 課程名稱︰離散數學課程性質︰系必修課程教師︰陳健輝開課學院：電資學院開課系所︰資訊系考試日期（年月日）︰2009/10/28 考試時限（分鐘）：120 是否需發放獎勵金：是（如未明確表示，則不予發放）試題 : 範圍:Combinatorics (For each problem, please provide your computation details, not only your answer.) 1. How many 8-digit quaternary (0, 1, 2, 3) sequences are there that they each contain exactly two 3's or none at all? (10%) 2. Solve a[n+2] - 6a[n+1] + 9a[n] = 3*2^n + 7*3^n for n>=0 3. Compute the number of integer solutions for x1+x2+x3+x4 = 24, where 4<=xi<=9 for i = 1, 2, 3, 4. (10%) 4. In how many ways can 24 bottles of soft drinks, 12 of type A and 12 of type B, be distributed among five surveyors so that each surveyor gets at least one bottle of type A and at least two bottles of type B? (10%) 5. Compute the number of ways to park motorcycles and compact cars in a row of n spaces, provided each cycle requires one space, each compact needs two, and all n spaces are used up. Assume that all cycles are identical in appearance, as are the cars. (10%) 6. In how many ways can one arrange all of the letters INFORMATION so that no pair of consecutive letters (i.e., "IN", "NI", "IO", "OI", "NO", and "ON") occurs twice? For example, IINNOOFRMTA and FORTMAIINON are counted, but INFORINMOTA and NORTFNOIAMI are not counted, because the latter two contain "IN" and "NO", respectively, twice. Notice that it is impossible that two "IN"s and two "NI"s (similarly, for "IN" and "IO", "IN" and "ON", "NI" and "OI", "NI" and "NO", "IO" and "OI", "IO" and "NO", "OI" and "ON", and "NO" and "ON") occur simultaneously. You are perprmitted to write your answer as a conbination of some factorials, e.g., 11!+7*10!+5*8!=2*6!. (10%) 7. Two dice, denoted by R and G, are rolled six times. Under the condition of (R, G)不屬於{(1,2), (1,3), (2,3), (2,4), (4,5), (5,5)}, compute the number of ways for each of R and G to occur 1,2,...,6(for example, (1,2), (3,3), (2,6), (5,5), (4,1), (6,4) and (5,4), (1,6), (6,3), (3,5), (4,2), (2,1) are two ways). (10%) 8. Define φ(n) to be the number of integers m so that 1<=m<=n and gcd(m, n) = 1, where n>=2 is an integer. For example, φ(2) = 1, φ(3) = 2, φ(4) = 2, and φ(5) = 4. Prove IN DETAIL that when n = (p1)^a *(p2)^b *(p3)^c, φ(n) = n(1-1/p1)(1-1/p2)(1-1/p3), where p1, p2, and p3 are three distinct prime numbers. (10%) 9. Pauline takes out a loan of 200,000 dollars that is to be paid back in 20 years with the interest rate 5% per year. The constant payment at the end of each year is (200,000/w)*([x*(1.05)^20]/[y*(1.05)^20 + z]). Please find w, x, y, and z. (10%) 10. Solve b[n+1] = b[n] + b[n-1] +...+b[1] + b[0] with n>=0 and b[0] = 1. (10%) 11. Please remember what (funny or impressive or encouraging or ..., but NOT RELATED TO DISCRETE MATHEMATICS) things did the professor Chen mention in the class. Write down any two of them. (10%) -- 心中有變數，就不用變數代換法 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.30.88

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