Description
Exercise 1: Multiplication (3 marks)
Write a program named multiplication.py that solves the multiplication
* * * x * * * —-* * * * * * * * * * * * ———-* * * * * *
in such a way that:
• each star stands for a digit, with the leftmost star on each line standing for a nonzero digit; • all digits on a given line are distinct; • the sum of all digits on a given line is the same for the 6 lines.
The output of your program should be of the form above, with of course the stars being replaced by appropriate digits. (Still it is irrelevant whether digits are separated by spaces, whether x is followed by spaces, whether there are leading spaces at the beginning of the last line, and the number of – on the separating lines is also irrelevant.)
Your program should not make any assumption on the actual solution, except obvious ones on the ranges of some values.
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Exercise 2: Pascal triangle (3 marks)
Write a program named pascal triangle.py that prompts the user for a nonnegative integer N and displays the first N + 1 rows of Pascal triangle. Below is a possible interaction. Make sure that the output is displayed exactly as shown.
$ python pascal_triangle.py Enter a nonnegative integer: zero Enter a nonnegative integer: 0 1 $ python pascal_triangle.py Enter a nonnegative integer: 1 1 1 1 $ python pascal_triangle.py Enter a nonnegative integer: 4 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 $ python pascal_triangle.py Enter a nonnegative integer: 8 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 $ python pascal_triangle.py Enter a nonnegative integer: 10 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1
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Exercise 3: Poker dice (4 marks)
Write a program named poker dice.py that simulates the roll of 5 dice, at most three times, as described at
http://en.wikipedia.org/wiki/Poker_dice
as well as a given number of rolls of the 5 dice to evaluate the probabilities of the various hands.
The next three pages show a possible interaction.
The following observations are in order.
• Your program has to define the functions play() and simulate(), but of course it will likely include other functions. • What is input from the keyboard is displayed in red; what is black is output by the program (in the pdf, for clarity, not at the prompt…). • The hands are displayed in the order Ace, King, Queen, Jack, 10 and 9. • All dice can be kept by inputting either all, or All, or the current hand in any order. • No die is kept by inputting nothing. • We have control over what is randomly generated by using the seed() function at the prompt, but do not make use of seed() in the program. • To roll a die, we use randint(0, 5) with 0, 1, 2, 3, 4 and 5 corresponding to Ace, King, Queen, Jack, 10 and 9, respectively.
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$ python Python 3.4.3 … from random import seed import poker_dice seed(0) poker_dice.play() The roll is: Ace Queen Jack Jack 10 It is a One pair Which dice do you want to keep for the second roll? all Ok, done. poker_dice.play() The roll is: Queen Queen Jack Jack Jack It is a Full house Which dice do you want to keep for the second roll? All Ok, done. poker_dice.play() The roll is: King King Queen 10 10 It is a Two pair Which dice do you want to keep for the second roll? King 10 Queen King 10 Ok, done. poker_dice.play() The roll is: Ace King Queen 10 10 It is a One pair Which dice do you want to keep for the second roll? 10 11 That is not possible, try again! Which dice do you want to keep for the second roll? ace That is not possible, try again! Which dice do you want to keep for the second roll? 10 10 The roll is: King 10 10 10 9 It is Three of a kind Which dice do you want to keep for the third roll? all Ok, done. poker_dice.play() The roll is: Ace Ace Queen 9 9 It is a Two pair Which dice do you want to keep for the second roll? Ace The roll is: Ace Ace Queen Jack 10 It is a One pair Which dice do you want to keep for the third roll? Ace The roll is: Ace Queen Queen Jack 10 It is a One pair
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seed(2) poker_dice.play() The roll is: Ace Ace Ace King Queen It is Three of a kind Which dice do you want to keep for the second roll? Ace Ace Ace The roll is: Ace Ace Ace 9 9 It is a Full house Which dice do you want to keep for the third roll? all Ok, done. poker_dice.play() The roll is: King Queen Queen 10 10 It is a Two pair Which dice do you want to keep for the second roll? The roll is: Ace King Jack 10 9 It is a Bust Which dice do you want to keep for the third roll? The roll is: Queen Jack 10 9 9 It is a One pair seed(10) poker_dice.play() The roll is: Ace Jack Jack 10 10 It is a Two pair Which dice do you want to keep for the second roll? Jack 10 Jack 10 The roll is: Ace Jack Jack 10 10 It is a Two pair Which dice do you want to keep for the third roll? Jack 10 Jack 10 The roll is: King Jack Jack 10 10 It is a Two pair seed(20) poker_dice.play() The roll is: King Queen 9 9 9 It is Three of a kind Which dice do you want to keep for the second roll? 9 King 9 9 The roll is: King 9 9 9 9 It is a Four of a kind Which dice do you want to keep for the third roll? 9 9 9 9 The roll is: Ace 9 9 9 9 It is a Four of a kind
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seed(0) poker_dice.simulate(10) Five of a kind : 0.00% Four of a kind : 0.00% Full house : 10.00% Straight : 0.00% Three of a kind: 0.00% Two pair : 20.00% One pair : 60.00% poker_dice.simulate(100) Five of a kind : 0.00% Four of a kind : 0.00% Full house : 3.00% Straight : 4.00% Three of a kind: 14.00% Two pair : 28.00% One pair : 45.00% poker_dice.simulate(1000) Five of a kind : 0.10% Four of a kind : 2.50% Full house : 3.80% Straight : 3.40% Three of a kind: 17.20% Two pair : 20.60% One pair : 46.30% poker_dice.simulate(10000) Five of a kind : 0.08% Four of a kind : 1.99% Full house : 3.93% Straight : 3.33% Three of a kind: 14.88% Two pair : 23.02% One pair : 46.58% poker_dice.simulate(100000) Five of a kind : 0.08% Four of a kind : 1.94% Full house : 3.85% Straight : 3.17% Three of a kind: 15.47% Two pair : 23.02% One pair : 46.31%
