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Using a combination of black square tiles and oblong tiles chosen from: red tiles measuring two units, green tiles measuring three units, and blue tiles measuring four units, it is possible to tile a row measuring five units in length in exactly fifteen different ways. How many ways can a row measuring fifty units in length be tiled? 길이 1인 정사각형 모양의 검은색 타일과 길이 2인 직사각형 모양의 빨간색 타일, 길이 3인 직사각형 모양의 초..

A row of five black square tiles is to have a number of its tiles replaced with colored oblong tiles chosen from red (length two), green (length three), or blue (length four). If red tiles are chosen there are exactly seven ways this can be done. If green tiles are chosen there are three ways. And of blue tiles are chosen there are two ways. Assuming that colors cannot be mixed there are 7+3+2=1..

Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 133468. 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. As \(n\) increases, the proportion of..