# Lesson 3 Problems 1-4
# Name: 4orty4
# Time: 4:00


##                Problem 1
## 7 * 3   +   9 * 1   +   20 * 1   ==   50
## 7 * 6   +   9 * 1   +   20 * 0   ==   51
## 7 * 1   +   9 * 5   +   20 * 0   ==   52
## 7 * 2   +   9 * 2   +   20 * 1   ==   52
## 7 * 5   +   9 * 2   +   20 * 0   ==   53
## 7 * 0   +   9 * 6   +   20 * 0   ==   54
## 7 * 1   +   9 * 3   +   20 * 1   ==   54
## 7 * 2   +   9 * 0   +   20 * 2   ==   54
## 7 * 4   +   9 * 3   +   20 * 0   ==   55

##              Problem 2
## For package sizes 6,9 and 20 six consecutive
## solutions prove that any higher number can
## also be purchased, because any combination can
## be increased by six by adding an additional
## package of six. For different package sizes,
## (n) consecutive solutions must be found, where
## (n) = the size of the smallest package.

##             Problems 3 and 4
## Solution condensed into one program. Tuple 'packages'
## can be changed to any other non-zero package sizes,
## provided the smallest package is listed first.

# packages[1]*x + packages[2]*y + packages[3]*z = n
# This program will find the highest whole number <200
# that can be purchased given the package sizes.

# Change package size by changing these values
# Smallest package size must be entered first for the program
# to function correctly
packages = (6,9,20)

#initialize values
total = 0
x, y, z = 0, 0, 0
n=0
solCounter = 0
isSolFound = 0
bestSoFar = 0

# For each x, y and z all values are tested between 0 and (n/package size + 1)

for n in range (1, 200):
    for x in range (0, (n/packages[0]+1)): 
        for y in range(0, (n/packages[1]+1)):
            for z in range(0, (n/packages[2]+2)):
                total = packages[0]*x + packages[1]*y + packages[2]*z
                if total == n:
                    print packages[0],'*',x,'  +  ',packages[1],'*',y,'  +  ',packages[2],'*',z,'  ==  ',total
                    isSolFound = 1
    #the loop continues even if a solution is found
    #not ideal but not sure how to break out of all 3 for loops
    #at once.

    if isSolFound == 1:
        solCounter += 1
        isSolFound = 0
    else:
        solCounter = 0
        bestSoFar = n # Stops when consecutive solutions = smallest package size
    if solCounter == packages [0]:
        break #breaks the loop so it doesn't have to try all 200 n's

print 'Package sizes are', packages[0], packages[1],'and', packages[2]               
print 'Largest number that can not be bought in exact quantity:', bestSoFar

prime = 3 
count = 1
divisor = 2 

while count<1000:
    while divisor<prime:  
        if prime%divisor == 0:
            divisor=prime+1
        else: divisor += 1

    if divisor == prime:   
        count += 1
        
    prime += 1              
    divisor=2                  
                                
print 'the 1000th prime is: ',prime-1   

# name game
# by: Jesse


print "Jesse's program! No big deal."
print "First things first, what's your last name?"
last = raw_input()
print "And your first name?"
first = raw_input()
print ("Got it! You are " + first + " " + last + "!")