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Problem 1 - Login security
In this problem, we'll create a login screen, where the user must enter a password in
order to see a secret message. We will give the user 3 chances to get the password right,
and either print the secret message or a failure message (after 3 chances).
First, define a function encrypt that takes one string. It will hash the string using the built-
in Python function hash (try it on the shell) and modulo the value by a prime number (e.g.
541 -- this is very small in the computer science world but good enough for us). The
function should then return this number.
e.g. encrypt("mypassword") -> 283 (if you use 541 as the prime, for example) At the top
of the file, define a variable _KEY to be the result, e.g. _KEY = 283.
Now, write the rest of the program. Each time you ask the user for the password, call
encrypt with the user's input, and compare the value to _KEY. If the two match, the user
(most likely) entered the correct password, otherwise he loses one chance.

Problem 2 - The game of Nims / Stones
In this game, two players sit in front of a pile of 100 stones. They take turns, each removing
between 1 and 5 stones (assuming there are at least 5 stones left in the pile). The person
who removes the last stone(s) wins.
Write a program to play this game. This may seem tricky, so break it down into parts. Like
many programs, we have to use nested loops (one loop inside another).
In the outermost loop, we want to keep playing until we are out of stones.
Inside that, we want to keep alternating players. You have the option of either writing two
blocks of code, or keeping a variable that tracks the current player. The second way is
slightly trickier since we haven't learned lists yet, but it's definitely do-able!
Finally, we might want to have an innermost loop that checks if the user's input is valid. Is
it a number? Is it a valid number (e.g. between 1 and 5)? Are there enough stones in the
pile to take off this many? If any of these answers are no, we should tell the user and re-
ask them the question.

So, the basic outline of the program should be something like this:
TOTAL = 100
MAX = 5
pile = TOTAL # all stones are in the pile to start while [pile is not empty]:
while [player 1's answer is not valid]: [ask player 1]
[check player 1's input... is it valid?] [same as above for player 2]
Note how the important numbers 100 and 5 are stored in a single variable at the top. This
is good practice -- it allows you to easily change the constants of a program. For example,
for testing, you may want to start with only 15 or 20 stones.
Be careful with the validity checks. Specifically, we want to keep asking player 1 for their
choice as long as their answer is not valid, BUT we want to make sure we ask them at least
ONCE. So, for example, we will want to keep a variable that tracks whether their answer is
valid, and set it to False initially.
When you're finished, test each other's programs by playing them!

Solution 1:
# Some constants...
LARGE_PRIME = 541
_KEY = 171 # to get this number, I used the password "solution"
MAX_FAILURES = 3 # stop when we hit this many failures
# The encrypt function. Remember, functions shouldn't be asking for input or
# printing their result. Any input a function needs (in this case, a string to
# encrypt) should be passed in, and the output should be returned.
def encrypt(text):
return hash(text) % LARGE_PRIME
# Main program code
num_failures = 0
# We'll keep looping until we hit the max number of failures...
# We need to break out of the loop when we get it correct also, see below.

while num_failures < MAX_FAILURES:
login = raw_input("Please enter the password: ")
if encrypt(login) == _KEY:
print "Correct!"
break # remember, this breaks out of the current loop
else:
num_failures = num_failures + 1
print "Incorrect! You have failed", num_failures, "times."
# When we get here, it's either because num_failures == MAX_FAILURES, or
# because we hit the break statement (i.e. we got the correct login), so...
if num_failures >= MAX_FAILURES:
print "Sorry, you have hit the maximum number of failures allowed."

#get a valid initial pile size
pile_size = int(raw_input("How many stones would you like to start with?n"))
while pile_size <= 0:
pile_size = int(raw_input("You need to start with at least one stone in the pile!n"))
#2 players; player 1 and player 2. Start with player 1
player = 1
#main game loop
while pile_size > 0:
prompt = "Player " + str(player) + ", there are " + str(pile_size) + " stones in front of you.
" +
"How many stones would you like to remove (1-5)?n"
move = int(raw_input(prompt))
if move <= 0:
print "Hey! You have to remove at least one stone!"
elif move > pile_size:
print "There aren't even that many stones in the pile..."
elif move > 5:
print "You can't remove more than five stones."
else:

#if we're here, they gave a valid move
pile_size = pile_size - move
player = 2-(player-1) #this is kind of cute: changes 1 to 2 and 2 to 1.
#If we've exited the loop, the pile size is 0. The player whose turn it is NOW just lost the
game..
print "Player", 2-(player-1), "has won the game!"
Solution 2: Nims 2
TOTAL = 100
MAX = 5
pile = TOTAL # number of stones in the pile at any given time
def is_valid(x):
# returns True iff x is between 1 and MAX, and there's also enough stones,
# otherwise returns False
return (x >= 1) and (x <= MAX) and (x <= pile)
while pile > 0:

# player 1 turn
print "Player 1's turn. There are", pile, "stones in the pile."
x = 0
while not is_valid(x):
# ask
x = int(raw_input("Player 1, how many? "))
# check
if not is_valid(x):
print "That's not valid, it has to be between 1 and 5, and",
"you can't pick up more than there are in the pile."
pile = pile - x
if pile == 0:
# win -- do something
print "Congratulations, Player 1, you win!"
break
# player 2 turn
print "Player 2's turn. There are", pile, "stones in the pile."
y = 0

while not is_valid(y):
y = int(raw_input("Player 2, how many? "))
if not is_valid(x):
print "That's not valid, it has to be between 1 and 5, and",
"you can't pick up more than there are in the pile."
pile = pile - y
if pile == 0:
# win -- do something
print "Congratulations, Player 2, you win!"
break
print "Game over."

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