project_euler.problem_112.sol1

Problem 112: https://projecteuler.net/problem=112

Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420. We shall call a positive integer that is neither increasing nor decreasing a “bouncy” number, for example, 155349. Clearly there cannot be any bouncy numbers below one-hundred, but just over half of the numbers below one-thousand (525) are bouncy. In fact, the least number for which the proportion of bouncy numbers first reaches 50% is 538. Surprisingly, bouncy numbers become more and more common and by the time we reach 21780 the proportion of bouncy numbers is equal to 90%.

Find the least number for which the proportion of bouncy numbers is exactly 99%.

Functions

check_bouncy(→ bool)

Returns True if number is bouncy, False otherwise

solution(→ int)

Returns the least number for which the proportion of bouncy numbers is

Module Contents

project_euler.problem_112.sol1.check_bouncy(n: int) → bool

Returns True if number is bouncy, False otherwise >>> check_bouncy(6789) False >>> check_bouncy(-12345) False >>> check_bouncy(0) False >>> check_bouncy(6.74) Traceback (most recent call last):

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ValueError: check_bouncy() accepts only integer arguments >>> check_bouncy(132475) True >>> check_bouncy(34) False >>> check_bouncy(341) True >>> check_bouncy(47) False >>> check_bouncy(-12.54) Traceback (most recent call last):

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ValueError: check_bouncy() accepts only integer arguments >>> check_bouncy(-6548) True

project_euler.problem_112.sol1.solution(percent: float = 99) → int

Returns the least number for which the proportion of bouncy numbers is exactly ‘percent’ >>> solution(50) 538 >>> solution(90) 21780 >>> solution(80) 4770 >>> solution(105) Traceback (most recent call last):

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ValueError: solution() only accepts values from 0 to 100 >>> solution(100.011) Traceback (most recent call last):

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ValueError: solution() only accepts values from 0 to 100