TheHedge

# Problem Set 2
# Name: TheHedge
# Collaborators: 0
# Time: 05:00:00

# PROBLEM 1
packages = (6,9,20)

def mcComboPossible(n):
    Possible = False
    for a in range (0,n):
        for b in range (0,n):
            for c in range (0,n):
                if (packages[0]*a) + (packages[1]*b) + (packages[2]*c) ==n:
                    Possible = True
                c += 1
            b += 1
        a += 1
    return Possible

def mcCombo(n):
    for a in range (0,n):
        for b in range (0,n):
            for c in range (0,n):
                if (packages[0]*a) + (packages[1]*b) + (packages[2]*c) ==n:
                    print 'to get' ,n, 'nuggets, you could buy ' ,a, 'x ', packages[0],' nuggets' ,b, 'x', packages[1],' nuggets, and' ,c, 'x ',packages[2],' nuggets'
                c += 1
            b += 1
        a += 1

numNuggets = int(raw_input('How many nuggets would you like? \n'))

if mcComboPossible(numNuggets) == False:
    print 'Sorry, that is not possible!'
else:
    mcCombo(numNuggets)

# PROBLEM 3
nCount =0

for a in range (6,100):
    if mcComboPossible(a) == True:
        nCount +=1
        if nCount == 6:
            print 'The largest number of McNuggets that cannot be bought in exact quantity is' ,a-6,' \n'  
    else:
        nCount = 0
        
# PROBLEM 4
limit = 50

def getMcCombos(limit,x,y,z):
    Possible = False
    for a in range (0,limit):
        for b in range (0,limit):
            for c in range (0,limit):
                if (packages[0]*a) + (packages[1]*b) + (packages[2]*c) ==limit:
                    Possible = True
                c += 1
            b += 1
        a += 1
    return Possible


while getMcCombos(limit,packages[0],packages[1],packages[2]) == True:
    limit -=1
    getMcCombos(limit,packages[0],packages[1],packages[2])
print 'Given package sizes ', packages[0],',', packages[1], 'and', packages[2],'the largest number of nuggets that connot be bought in the exact quantity is', limit,
    

# Problem Set 1
# Name: TheHedge
# Collaborators: 0
# Time: ~03:00:00

# Part A

c = 1                       # use this to count the number of primes
a = 3                       # test value, starting at 3 as 1 & 2 are primes
d = 1000                    # set the number of the prime we want

while (c < d):              # only run if the # of primes is less than d
    b = a/2                 # what is the remainder if divided by 2?
    while (b > 1):          # if there is no remainder, its not a prime
        if a % b == 0:      # if it is not a prime...
            a = a + 2       # set a to the next odd number
            b = a / 2       # what is the remainder if divided by 2?
        else: b = b - 1     # a is a prime, so 
    c = c + 1               # increase the count of primes by 1
    a = a + 2               # go to the next odd number
print a - 2                 # now that the 1000th prime is known, show its value

# Part B

import math                                     # get the math tools
a = 3
c = 1                                           # counter
d = int (raw_input("Enter a Number: "))         # user inputs a value
e = math.log(2)                                 # the log of 2, the starting point

while a < d:                                    # only run when primes are less than d
    b = 3                                       # we start with 3
    while (b < math.sqrt(a) and a % b <> 0):    # do this for values where b < sqrt(a) and for primes
        b = b + 2                               # set b to the next 
    if b > math.sqrt(a):                    
        e = e + math.log(a)                     # add the log of a to e
    a = a + 2                                   # go to the next odd number
print e                                         # the sum of the logs of the primes
print a                                         # the number chosen
r = e / a                                       # calculate the ratio of e to a
print r                                         # print the ratio of e to a

# Problem Set 0
# Name: TheHedge
# Collaborators: 0
# Time: 00:01:00

firstName = raw_input('Enter your first name:')
lastName = raw_input('Enter your last name:')

print firstName + " " + lastName