mgoff11

#Problem Set 2a
#Michael

a=6
b=9
c=20
candidate=0
bestSoFar=1

for n in range(1,50):
    for i in range(0,n/a+1):
        for j in range(0,n/b+1):
            for k in range(0,n/c+1):
                if a*i+b*j+c*k==n:
                    break
            if a*i+b*j+c*k==n:
                break
        if a*i+b*j+c*k==n:
            break
    if a*i+b*j+c*k==n:
        candidate+=1
    else:
        candidate=0
        bestSoFar=n
    if candidate==6:
        break

print 'Largest number of McNuggets that cannot be bought in exact quantity: '+str(bestSoFar)
        







#Problem Set 2b
#Michael 

bestSoFar = 0     
                  
packages = (2,4,6)   
a=packages[0]
b=packages[1]
c=packages[2]

for n in range(1, 150):   
    for i in range(0,n/a+1):
        for j in range(0,n/b+1):
            for k in range(0,n/c+1):
                if a*i+b*j+c*k==n:
                    break
            if a*i+b*j+c*k==n:
                break
        if a*i+b*j+c*k==n:
            break
    if a*i+b*j+c*k==n:
        candidate+=1
    else:
        candidate=0
        bestSoFar=n
    if candidate==a:
        break

if candidate<a:
    print 'The largest number of McNuggets that cannot be bought in exact quantity is greater than 150.'
else:
    print 'Given package sizes '+str(a)+', '+str(b)+', and '+str(c)+', the largest number of McNuggets that cannot be bought in exact quantity is: '+str(bestSoFar)

        
        
            

#Problem Set 1
#Michael 

prime = 3
count = 1
divisor = 2

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

    if divisor == prime:
        count+=1                                #same as count=count+1

    prime+=2
    divisor=2

print 'The 1000th prime is: ',prime-2










from math import*

prime = 3
divisor = 2
n = 1000
logsum = log(2)

while prime<n-1:
    while divisor<prime:
        if prime%divisor == 0:
            divisor = prime+1
        else: divisor = divisor+1

    if divisor == prime:
        logsum+=log(prime)

    prime+=2
    divisor=2

print 'The sum of the logarithms of all the primes less than n is ', logsum
print 'The number n is ', n
print 'The ratio of the sum of the logarithms to n is ', logsum/n

#Problem Set 0
#Michael 

lastname = raw_input("What is your last name?")
firstname = raw_input("What is your first name?")
print firstname, lastname