n! means n * (n – 1) * … * 3 * 2 * 1
Find the sum of the digits in the number 100!
['9332621544394415268169923885626670049071596826438162146859296389521759999 32299156089414639761565182862536979208272237582511852109168640000000000000 00000000000']
So 100! gives you a long number, what the question is asking is to sum each digit in that long number.
sumu = 1
for i in range(1, 101):
sumu = sumu * i
x = str(sumu)
temp = 0
for i in x:
temp = temp + int(i)
print temp
The objective of this lab is to learn how to use functions to implement a solitaire version of a game called Pig. In Pig Solitaire, our objective is to reach a given goal score g within n turns. For example, you win the game if you score 100 points within 5 turns. Or, 50 points within 2 turns. You get to set the game parameters. In Pig Solitaire, during each turn, a player repeatedly rolls a die until either a 1 is rolled or the player holds and scores the sum of the rolls (i.e., the turn total). At any time during a player’s turn, the player is faced with two choices: roll or hold. If the player rolls a 1, the player scores nothing and a new turn begins. If the player rolls a number other than 1, the number is added to the player’s turn total and the player’s turn continues. If the player instead chooses to hold, the turn total is added to the player’s score and a new turn begins
Pig Solitaire 1. Design and implement a Python program to implement Pig Solitaire. Your program must use the following three functions: (a) roll_die()—returns the result of a single roll of the die. (b)play_single_turn(total)—plays a single turn of Pig Solitaire and returns the number of points the player achieved on this turn. This function expects a value that will be stored in the parameter total, which denotes the total number of points the player has achieved so far. (c) main()—the foundation of the program and contains all of the code that does not appear in the roll_die or play_single_turn functions.
import random
g = input('How many points to win?: ')
n = input('What is the maximum number of turns?: ')
def roll_die():
# Roll the die
return random.randint(1,6)
def play_single_turn(total):
# Play a single turn
play = 'y'
turn_total = 0
while play != 'h':
y = roll_die()
if y == 1:
# Turn over - got a 1!
turn_total = 0
print "Total points:\t", total
print "Roll:\t", y
print "Your turn is over!"
print "Turn total: \t", turn_total
print raw_input("Press <Enter> to continue... ")
play = 'h'
else:
# Play turn
turn_total = turn_total + y
print "Total points:\t", total
print "Roll:\t", y
print "Turn total: \t", turn_total
play = raw_input("Press <Enter> to roll again or 'h' to hold: \n")
return turn_total
def main():
total = 0
turn = 1
while turn <= n:
print "\n*** TURN %s ***\n" % turn
turn += 1
x = play_single_turn(total)
print "Total points = ", x
total = total + x
if total >= g:
print "\nYOU WIN!"
print "It took you %s turns to reach %s points." % ((turn-1),g)
break
else:
continue
else:
print "\nYOU LOSE!"
print "You failed to reach %s points in %s turns." % (g,(turn-1))
if __name__ == '__main__':
main()
How many points to win?: 50
What is the maximum number of turns?: 3
*** TURN 1 ***
Total points: 0
Roll: 2
Turn total: 2
Press to roll again or 'h' to hold:
Total points: 0
Roll: 5
Turn total: 7
Press to roll again or 'h' to hold:
Total points: 0
Roll: 3
Turn total: 10
Press to roll again or 'h' to hold:
Total points: 0
Roll: 6
Turn total: 16
Press to roll again or 'h' to hold:
h
Total points = 16
*** TURN 2 ***
Total points: 16
Roll: 1
Your turn is over!
Turn total: 0
Press to continue...
Total points = 0
*** TURN 3 ***
Total points: 16
Roll: 4
Turn total: 4
Press to roll again or 'h' to hold:
Total points: 16
Roll: 1
Your turn is over!
Turn total: 0
Press to continue...
Total points = 0
YOU LOSE!
You failed to reach 50 points in 3 turns.
>>>
How many points to win?: 50
What is the maximum number of turns?: 3
*** TURN 1 ***
Total points: 0
Roll: 3
Turn total: 3
Press to roll again or 'h' to hold:
Total points: 0
Roll: 2
Turn total: 5
Press to roll again or 'h' to hold:
Total points: 0
Roll: 3
Turn total: 8
Press to roll again or 'h' to hold:
Total points: 0
Roll: 6
Turn total: 14
Press to roll again or 'h' to hold:
Total points: 0
Roll: 5
Turn total: 19
Press to roll again or 'h' to hold:
Total points: 0
Roll: 3
Turn total: 22
Press to roll again or 'h' to hold:
h
Total points = 22
*** TURN 2 ***
Total points: 22
Roll: 2
Turn total: 2
Press to roll again or 'h' to hold:
Total points: 22
Roll: 4
Turn total: 6
Press to roll again or 'h' to hold:
Total points: 22
Roll: 5
Turn total: 11
Press to roll again or 'h' to hold:
Total points: 22
Roll: 4
Turn total: 15
Press to roll again or 'h' to hold:
Total points: 22
Roll: 4
Turn total: 19
Press to roll again or 'h' to hold:
h
Total points = 19
*** TURN 3 ***
Total points: 41
Roll: 5
Turn total: 5
Press to roll again or 'h' to hold:
Total points: 41
Roll: 2
Turn total: 7
Press to roll again or 'h' to hold:
Total points: 41
Roll: 6
Turn total: 13
Press to roll again or 'h' to hold:
h
Total points = 13
YOU WIN!
It took you 3 turns to reach 50 points.
Original link
The objective of this lab is to learn how to use functions to implement a solitaire version of a game called Pig. In Pig Solitaire, our objective is to reach a given goal score g within n turns. For example, you win the game if you score 100 points within 5 turns. Or, 50 points within 2 turns. You get to set the game parameters. In Pig Solitaire, during each turn, a player repeatedly rolls a die until either a 1 is rolled or the player holds and scores the sum of the rolls (i.e., the turn total). At any time during a player’s turn, the player is faced with two choices: roll or hold. If the player rolls a 1, the player scores nothing and a new turn begins. If the player rolls a number other than 1, the number is added to the player’s turn total and the player’s turn continues. If the player instead chooses to hold, the turn total is added to the player’s score and a new turn begins.
Pig Solitaire 2. Design and implement a Python program to implement Pig Solitaire to maximize one’s score in n turns.
from __future__ import division
import random
n = input('What is the maximum number of turns?: ')
def roll_die():
# Roll the die
return random.randint(1,6)
def play_single_turn(total):
# Play a single turn
play = 'y'
turn_total = 0
while play != 'h':
y = roll_die()
if y == 1:
# Turn over - got a 1!
turn_total = 0
print "Total points:\t", total
print "Roll:\t", y
print "Your turn is over!"
print "Turn total: \t", turn_total
print raw_input("Press <Enter> to continue... ")
play = 'h'
else:
# Play turn
turn_total = turn_total + y
print "Total points:\t", total
print "Roll:\t", y
print "Turn total: \t", turn_total
play = raw_input("Press <Enter> to roll again or 'h' to hold: \n")
return turn_total
def main():
total = 0
turn = 1
while turn <= n:
print "\n*** TURN %s ***\n" % turn
turn += 1
x = play_single_turn(total)
print "Total points = ", x
total = total + x
avg = total/n
else:
print "\n***GAME SUMMARY***"
print "With %s turns, you reached %s points." % (n,total)
print "Average points per turn: %s\n" % avg
if __name__ == '__main__':
main()
What is the maximum number of turns?: 5
*** TURN 1 ***
Total points: 0
Roll: 4
Turn total: 4
Press to roll again or 'h' to hold:
Total points: 0
Roll: 3
Turn total: 7
Press to roll again or 'h' to hold:
Total points: 0
Roll: 1
Your turn is over!
Turn total: 0
Press to continue...
Total points = 0
*** TURN 2 ***
Total points: 0
Roll: 5
Turn total: 5
Press to roll again or 'h' to hold:
Total points: 0
Roll: 4
Turn total: 9
Press to roll again or 'h' to hold:
Total points: 0
Roll: 1
Your turn is over!
Turn total: 0
Press to continue... h
h
Total points = 0
*** TURN 3 ***
Total points: 0
Roll: 6
Turn total: 6
Press to roll again or 'h' to hold:
Total points: 0
Roll: 6
Turn total: 12
Press to roll again or 'h' to hold:
Total points: 0
Roll: 4
Turn total: 16
Press to roll again or 'h' to hold:
h
Total points = 16
*** TURN 4 ***
Total points: 16
Roll: 1
Your turn is over!
Turn total: 0
Press to continue...
Total points = 0
*** TURN 5 ***
Total points: 16
Roll: 2
Turn total: 2
Press to roll again or 'h' to hold:
Total points: 16
Roll: 4
Turn total: 6
Press to roll again or 'h' to hold:
Total points: 16
Roll: 1
Your turn is over!
Turn total: 0
Press to continue...
Total points = 0
***GAME SUMMARY***
With 5 turns, you reached 16 points.
Average points per turn: 3.2
Original link
This problem was similar to Project Euler’s # 17 so I decided to solve it.
Can anyone solve this using functions?
Integer to English conversion. Given an integer value,
return a string with the equivalent Englist text of each digit.
For example, an input of 89 results in “eight-nine” being
returned. For an extra challenge, return English text with
proper usage, i.e., “eighty-nine.” For this problem, restrict
values to be between 0 and 1,000.
number = {
1:'one',2:'two',3:'three',4:'four',5:'five',6:'six',7:'seven',
8:'eight',9:'nine',10:'ten',11:'eleven',12:'twelve',13:'thirteen',
14:'fourteen',15:'fifteen',16:'sixteen',17:'seventeen',
18:'eighteen',19:'nineteen',20:'twenty',30:'thirty',40:'fourty',
50:'fifty',60:'sixty',70:'seventy',80:'eighty',90:'ninety',
100:'hundred',1000:'thousand'}
x = input('Please enter an number between 1 and 1000: ')
x1 = str(x)
if len(x1) == 1:
# If user enters a number between 1-9
print "Integer in English is: ", number[x]
elif len(x1) == 2:
# If user enters a number between 10-99
x2 = x1[0:1]
x3 = x1[1:2]
if x < 20:
# Consider numbers less than 20
print "Integer in English is: ", number[x]
elif x2 != '0' and x3 == '0':
# Consider multiples of 10: 20, 30 ...
print "Integer in English is: ", number[x]
else:
# Consider all other numbers less than 100
x4 = str(x2 + '0')
print "Integer in English is:", number[int(x4)] + \
'-' + number[int(x3)]
elif len(x1) == 3:
# If user enters a number between 100-999
x2 = x1[0:1]
x3 = x1[1:2]
x4 = x1[2:3]
x5 = (x3 + x4)
x6 = x3 + '0'
if x3 == '0' and x4 == '0':
# Consider the 100, 200, 300 numbers ...
print "Integer in English is:", number[int(x2)] \
+ '-' + number[100]
elif x3 == '0' and x4 != '0':
# Consider 101-109, 201-209, ...
print "Integer in English is:", number[int(x2)]+ \
'-' + number[100] + ' and ' + number[int(x4)]
elif x3 != '0' and x4 == '0':
# Consider 110,120,130, 210,220,230 ...
print "Integer in English is:", number[int(x2)] \
+ '-' + number[100] + ' and ' + number[int(x5)]
elif x3 == '1' and x4 != '0':
# Consider the teens 111-119, 211-219 ...
print "Integer in English is:", number[int(x2)] \
+ '-' + number[100] + ' and ' + number[int(x5)]
else:
# Consider all other 3 digit numbers
print "Integer in English is:", number[int(x2)] \
+ '-' + number[100] + ' and ' + number[int(x6)] \
+ '-' + number[int(x4)]
elif len(x1) == 4 and x == 1000:
# If user enters 1000
print "Integer in English is:", number[1] + '-' + number[1000]
else:
# If user enters something other than a number from 1-1000
print "Please try again"
Thanks to a nice comment from a gentleman – Adam… He pointed out that the correct spelling for ‘fourty’ is ‘forty’. The answer now comes out to be 21124.
I did this problem twice and came up with a total of 21224 each time. The correct answer is supposed to be 21124.
If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.
If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?
NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of “and” when writing out numbers is in compliance with British usage.
number = {
1:'one',2:'two',3:'three',4:'four',5:'five',6:'six',7:'seven',
8:'eight',9:'nine',10:'ten',11:'eleven',12:'twelve',13:'thirteen',
14:'fourteen',15:'fifteen',16:'sixteen',17:'seventeen',
18:'eighteen',19:'nineteen',20:'twenty',30:'thirty',40:'forty',
50:'fifty',60:'sixty',70:'seventy',80:'eighty',90:'ninety',
100:'hundred',1000:'thousand'}
tally = 0
for n in range(1,1001):
x = str(n)
if len(str(n)) == 1:
# The first 9 numbers are 1 digit -- in the dictionary
k = len(number[n])
print "n= %s k= %s" %(n,k)
elif len(str(n)) == 2:
x1 = x[0:1]
x2 = x[1:2]
if n < 20:
# The numbers under 20 -- in the dictionary
k = len(number[n])
print "n= %s k= %s" %(n,k)
else:
if x2 == '0':
# The numbers under 100 and greater than 19 -- in the
# dictionary ending in '0', (20, 30, 40 ....)
k = len(number[n])
print "n= %s k= %s" %(n,k)
else:
# The other numbers under 100 greater than 19
x1a = str(x1 + '0')
k = len(number[int(x1a)]) + len(number[int(x2)])
print "n1= %s k1= %s" %(n,k)
elif len(str(n)) == 3:
# add 3 for 'and' i.e. -- two-hundred and ten
x1 = x[0:1]
x2 = x[1:2]
x3 = x[2:3]
x1a = str(x2 + '0')
x1aa = str(x2 + x3)
if x1 == '1' and x2 == '0' and x3 == '0':
# 100 -- in the dictionary
k = len(number[1]) + len(number[100])
print "n= %s k= %s" %(n,k)
elif x2 == '0' and x3 == '0':
# Consider 200, 300, 400, 500, 600, 700, 800, and 900
k = len(number[int(x1)]) + len(number[100])
print "n= %s k= %s" %(n,k)
elif x2 == '0' and x3 != '0':
# Consider 101, 102 ... 109, 201, 202, ... 209 etc.
k = 3 + len(number[int(x1)]) + len(number[100]) \
+ len(number[int(x3)])
print "n= %s k= %s" %(n,k)
elif x2 != '0' and x3 == '0':
# Consider 110, 120, ... 190, 210, 220, ... 290 etc.
k = 3 + len(number[int(x1)]) + len(number[100]) \
+ len(number[int(x1a)])
print "n= %s k= %s" %(n,k)
elif x2 == '1' and x3 != '0':
# Consider the teens 111, 112, ... 119, 211, 212, ... 219 etc.
k = 3 + len(number[int(x1)]) + len(number[100]) \
+ len(number[int(x1aa)])
print "n= %s k= %s" %(n,k)
else:
# Consider all the other numbers
k = 3 + len(number[int(x1)]) + len(number[100]) \
+ len(number[int(x1a)]) + len(number[int(x3)])
print "n= %s k= %s" %(n,k)
else:
# 1000 -- two parts (one and thousand) -- in the dictionary
k = len(number[1]) + len(number[1000])
print "n= %s k= %s" %(n,k)
tally = tally + k
print "Tally = %s" % tally
This took a minute or so to run on my PC. My print checkpoints are included
The following iterative sequence is defined for the set of positive integers:
n –> n/2 (n is even)
n –> 3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following sequence:
13 –> 40 –> 20 –> 10 –> 5 –> 16 –> 8 –> 4 –> 2 –> 1
It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
NOTE: Once the chain starts the terms are allowed to go above one million.
largest = 0
for n in range(2, 1000001):
counter = 1
number = n
while n > 1:
if n%2 == 0:
n = n/2
counter += 1
else:
n = n*3 + 1
counter += 1
if counter > largest:
largest = counter
print "largest = ", largest
print "starting number = ", number
Python can handle these large number (50 digits and their addition) without any special handling
My print checkpoints are included
Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.
f = open('one-hundred_50.txt', 'rU')
tally = 0
for g in f.readlines():
gpl = g.replace('\n', '')
if gpl.isdigit():
number = int(gpl)
print "number= ", number
tally = number + tally
else:
print "The varialble gpl contains no digit"
f.close()
print "tally= ", tally | Greg Christian on Project Euler – Problem … |
 | Arnav on Project Euler – Problem … |
| Greg Christian on Project Euler – Problem … |
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| Dave on Project Euler – Problem … |
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