project_euler.problem_092.sol1

Project Euler Problem 092: https://projecteuler.net/problem=92 Square digit chains A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before. For example, 44 → 32 → 13 → 10 → 1 → 1 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89 Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89. How many starting numbers below ten million will arrive at 89?

Attributes

CHAINS
DIGITS_SQUARED

Functions

chain(→ bool)	The function generates the chain of numbers until the next number is 1 or 89.
next_number(→ int)	Returns the next number of the chain by adding the square of each digit
solution(→ int)	The function returns the number of integers that end up being 89 in each chain.

Module Contents

project_euler.problem_092.sol1.chain(number: int) → bool

The function generates the chain of numbers until the next number is 1 or 89. For example, if starting number is 44, then the function generates the following chain of numbers: 44 → 32 → 13 → 10 → 1 → 1. Once the next number generated is 1 or 89, the function returns whether or not the next number generated by next_number() is 1. >>> chain(10) True >>> chain(58) False >>> chain(1) True

project_euler.problem_092.sol1.next_number(number: int) → int

Returns the next number of the chain by adding the square of each digit to form a new number. For example, if number = 12, next_number() will return 1^2 + 2^2 = 5. Therefore, 5 is the next number of the chain. >>> next_number(44) 32 >>> next_number(10) 1 >>> next_number(32) 13

project_euler.problem_092.sol1.solution(number: int = 10000000) → int

The function returns the number of integers that end up being 89 in each chain. The function accepts a range number and the function checks all the values under value number.

>>> solution(100)
80
>>> solution(10000000)
8581146

project_euler.problem_092.sol1.CHAINS: list[bool | None]

project_euler.problem_092.sol1.DIGITS_SQUARED