Project Euler

Problem

This problem comes from Project Euler 17

Problem

If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.

If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?

NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of “and” when writing out numbers is in compliance with British usage.

Code

# Project Euler: Problem 17
# Number Letter Counts

# Words
ones = len("onetwothreefourfivesixseveneightnine")
teens = len("teneleventwelvethirteenfourteenfifteensixteenseventeeneighteennineteen")
tens = len("twentythirtyfourtyfiftysixtyseventyeightyninety")
hundred = len("hundred")
and_ = len("and")

# Below 100
below_100 = 0
below_100 += ones                               # 1-9
below_100 += teens                              # 10-19
below_100 += tens*10 + ones*8                   # 20-99

# Hundreds
hundreds = 0
hundreds += ones + hundred*9                    # 100, 200, 300...
hundreds += ones*99 + (hundred + and_)*99*9     # "one hundred and ...", "two hundred and ..."
hundreds += below_100*9                         # below_100 is repeated 9 times

print(below_100 + hundreds + len("onethousand"))

Solution

The solutions is split into three sections

1. # Words. I made word “groups” for the numbers that are commonly used
2. # Below 100. Self-explanatory. From 1-99
3. # Hundreds. Self-explanatory. From 100-999

From there, it’s combining these groups of words to make all the numbers from 1 to 999 (then appending one thousand to the end).

Below 100

Most of this is self-explanatory, but below_100 += tens*10 + ones*8. We have tens*10 because we say, for example, “twenty, twenty-one, twenty-two, … twenty-nine,” etc. You may notice that the word “twenty” is said ten times.

We have ones*8 because that group of words is only used eight times: from twenty to ninety. (One to nine are already accounted for earlier with below_100 += ones)

Hundreds

This one is a bit more complicated.

hundreds += ones + hundred*9 are for the words 100, 200, 300, … because those numbers do not have “and” in them.

hundreds += ones*99 + (hundred + and_)*99*9 counts how many times we say “one hundred and”, “two hundred and”, “three hundred and”, etc.

The rest is self-explanatory.