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+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%.