Problem 42377. Bouncy numbers

Inspired by Project Euler n°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 surprisingly, these numbers become more and more common after.

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

As always this type of problem is difficult to solve with usual Matlab functions (num2str).

So keep an eye on time...

Solution Stats

70.59% Correct | 29.41% Incorrect
Last solution submitted on Apr 02, 2019

Problem Comments