Unformatted text preview: n = 36. Q4. Let d be a positive integer. Show that among any group of d + 1 (not necessary consecutive) integers there are two with exactly the same remainder when they are divided by d . Answer Any number i when divided by d gives a remainder r where 0 ≤ r < d . Since we have d + 1 integers and d possible remainders, there will be at least ⌈ d +1 d ⌉ = 2 integers with the same remainder. Q5. How many subsets with more than two elements does a set with 15 elements have? Answer The total number of subsets = 2 15 . The number of subsets with 0 element is 1, with 1 element is 15, and with 2 elements is C(15 , 2) = (15 × 14) / 2! = 105. Therefore, the number of subsets with more than two elements = 2 15 − (1 + 15 + 105) = 32 , 647. 1...
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 Fall '08
 W.Szpankowski
 Natural number, decimal digits, significant digit

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