#Problem Set 2
#Name: Nick
#Time: 00:10
#Collaborators: None

#Problem 1
region = range(50, 55)

for a in range (0, 20):
        for b in range(0,20):
                for c in range(0,20):
                        k = 6 * a + 9 * b + 20 * c;
                        if k in region:
                                print("{0:2}*6 + {1}*9 + {2}*20 = {3}".format(a,b,c,k));

#       2*6 + 2*9 + 1*20 = 50
#       5*6 + 1*9 + 0*20 = 51
#       2*6 + 0*9 + 2*20 = 52
#       1*6 + 3*9 + 1*20 = 53   
#       9*6 + 0*9 + 0*20 = 54
#       1*6 + 1*9 + 2*20 = 55

#Problem 2
"""
        Theorem is true because when we had all x, x+1,..., x+5 all next steps will repeat.
        For example if we has 54 nugets we can add 6 and get 60 or 51 + 6 =57.
        This works for any x, ...,  x+5 values
"""

#Problem 3
def can_buy(n, ax, bx, cx):
        for a in range(0,20):
                for b in range(0,20):
                        for c in range(0,20):
                                k = ax * a + bx * b + cx * c
                                if k == n:
                                        return True
        return False

def solve(a,b,c):
        count = 0
        for n in range(1,200):
                if not can_buy(n,a,b,c):
                        ans = n
                        count = 0
                else:   count += 1
                if count == 6:  break
        print("Given package sizes <{0}>, <{1}>, <{2}>, the largest number of McNuggets that cannot be bought in exact quantity is: {3}".format(a,b,c,ans))


solve(6,9,20)

#Problem 4
solve(10,14,15)

#Problem Set 1 
#Name: Nick
#Collaborators: None
#Time: 1 day

import math

first_prime = 2
max_prime_count = 1000
count = 1
next_prime = first_prime + 1
count = count + 1
while (count < max_prime_count):
    next_prime = next_prime + 2
    stop_value = math.sqrt(next_prime)
    is_prime = True
    value = 2
    while (value <= stop_value):
        if (next_prime%value == 0):
            is_prime = False
            value = stop_value+1
        else: value = value + 1
    if (is_prime):
        count = count + 1
        #print count, ': ', next_prime
print 'The 1000th prime is ' + str(next_prime)


#2

from math import *
first_prime = 2
max_prime_count = raw_input('How many prime numbers:   ')
count = 1
log_sum = log(first_prime)
next_prime = first_prime + 1
count = count + 1
log_sum = log_sum + log(next_prime)
while (count < int(max_prime_count)):
    next_prime = next_prime + 2
    stop_value = sqrt(next_prime)
    is_prime = True
    value = 2
    while (value <= stop_value):
        if (next_prime%value == 0):
            is_prime = False
            value = stop_value+1
        else: value = value + 1
    if (is_prime):
        log_sum = log_sum + log(next_prime)
        count = count + 1
        ratio = next_prime/log_sum
print count, ': ', next_prime, log_sum, ratio

#Problem Set 0
#Name: Nick
#Collaborators: None
#Time: 5 Minutes

#User inputs first name
First=raw_input("Enter your first name:  ")
#User inputs last name
Last=raw_input("Enter your last name:  ")
#prints
print First,Last