Day003NumberCrosswords.sagews

Author: Vincent J. Matsko
Date: 7 September 2015, Day003
Post: CrossNumber Puzzles

# Here is the code to easily create lists of numbers with certain properties.
# To make some changes, save this file in one of your own projects.
# Then change the numbers as you wish.  
# Remember, to evaluate, hold down th

for i in range(10,22):
    print i, i^3;

10 1000 11 1331 12 1728 13 2197 14 2744 15 3375 16 4096 17 4913 18 5832 19 6859 20 8000 21 9261

for i in range(6,10):
    print i, i^4;

6 1296 7 2401 8 4096 9 6561

# Gets the third digit from the right using integer division and modular arithmetic.
def get_third(n):
    return (n // 100) % 10

get_third(34)

0

get_third(123456789)

7

# Generalizes the function get_third.
# The power of 10 we need comes from the digit that we want.
def get_which(n, digit):
    return (n // 10^(digit - 1)) % 10

get_which (987654321,6)

6

# To get digits from the left, it may be helpful to know how many digits a number has.
# You can use logarithms for this, or use this simple recursive function.
# Assume that n is an integer (to avoid error-checking).
def how_many(n):
    if n < 10:
        return 1
    else:
        return 1 + how_many(n // 10);

how_many(3)

1

how_many(123456789)

9