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3.11 The Mathematica function IntegerDigits returns a list containing the digits of an integer. How many digits are there in 100! and what is the 50th digit from the left and from the right
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list = IntegerDigits[100!] {9, 3, 3, 2, 6, 2, 1, 5, 4, 4, 3, 9, 4, 4, 1, 5, 2, 6, 8, 1, 6, 9, 9, 2, 3, 8, 8, 5, 6, 2, 6, 6, 7, 0, 0, 4, 9, 0, 7, 1, 5, 9, 6, 8, 2, 6, 4, 3, 8, 1, 6, 2, 1, 4, 6, 8, 5, 9, 2, 9, 6, 3, 8, 9, 5, 2, 1, 7, 5, 9, 9, 9, 9, 3, 2, 2, 9, 9, 1, 5, 6, 0, 8, 9, 4, 1, 4, 6, 3, 9, 7, 6, 1, 5, 6, 5, 1, 8, 2, 8, 6, 2, 5, 3, 6, 9, 7, 9, 2, 0, 8, 2, 7, 2, 2, 3, 7, 5, 8, 2, 5, 1, 1, 8, 5, 2, 1, 0, 9, 1, 6, 8, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} Length[list] 158 Part[list, 50] or list[[50]] 1 Part[list, 50] or list[[ 50]] 2
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3.12 Compute the sum of the digits of the 100th Fibonacci number.
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We use IntegerDigits (see previous problem). list = IntegerDigits[Fibonacci[100]] {3, 5, 4, 2, 2, 4, 8, 4, 8, 1, 7, 9, 2, 6, 1, 9, 1, 5, 0, 7, 5}
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Length[list]
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Sum[list[[k]], {k, 1, Length[list]] or 93
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list[[k]]
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3.13 The command Table[i*j,{i, 3, 10},{j, 2, 7}] generates a nested list of numbers. Add the fourth number in the fifth sublist to the third number in the sixth sublist.
SOLUTION
list = Table[i*j,{i, 3, 10},{j, 2, 7}]
Lists
{{6,
9, 12, 15, 18, 21}, {8, 12, 16, 20, 24, 28}, {10, 15, 20, 25, 30, 35}, 18, 24, 30, 36, 42},{14, 21, 28, 35, 42, 49}, {16, 24, 32, 40, 48, 56}, {18, 27, 36, 45, 54, 63}, {20, 30, 40, 50, 60, 70}}
{12,
list[[5, 4]] + list[[6, 3]] 67
35 + 32 = 67
3.14 The Mathematica function RealDigits returns a list containing a list of the digits of an approximate real number followed by the number of digits that are to the left of the decimal point. Compute a 15 significant digit approximation of and determine the next to the last decimal digit.
SOLUTION
approx = N[Pi,15] 3.14159265358979 list = RealDigits[approx] {{3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9}, 1} list[[1, 2]] 7
3.15 Construct a list consisting of the consecutive integers from 1 to 10 followed by the consecutive integers from 20 to 30.
SOLUTION 1
Drop[Range[30], {11, 19}] {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
SOLUTION 2
Join[Range[1, 10], Range[20, 30]]
2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
3.16 Construct a list consisting of the consecutive integers 1 to 10, followed by 99, followed by 11 to 20.
SOLUTION
Insert[Range[20], 99, 11] {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 99, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
3.17 Construct a list of the integers 1 to 20 in descending order.
SOLUTION 1
Range[20, 1, 1] {20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}
SOLUTION 2
{20,
Range[20]//Reverse This is equivalent to Reverse [Range [20]]. 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}
3.18 Sort the letters of the word MISSISSIPPI alphabetically.
SOLUTION
list = Characters["MISSISSIPPI"] {M,I,S,S,I,S,S,I,P,P,I} Sort[list] {I, I, I, I, M, P, P, S, S, S, S}
Lists
3.19 Construct a list of numbers from 0 to 2 in increments of / 6.