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P22 [Combinatorics] - Turkish NMO 1st Round - 2001

Source:

April 20, 2014
geometryrectangle

Problem Statement

A ladder is formed by removing some consecutive unit squares of a 10×1010\times 10 chessboard such that for each kk-th row (k{1,2,,10}k\in \{1,2,\dots, 10\}), the leftmost k1k-1 unit squares are removed. How many rectangles formed by composition of unit squares does the ladder have?
<spanclass=latexbold>(A)</span> 625<spanclass=latexbold>(B)</span> 715<spanclass=latexbold>(C)</span> 1024<spanclass=latexbold>(D)</span> 1512<spanclass=latexbold>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 625 \qquad<span class='latex-bold'>(B)</span>\ 715 \qquad<span class='latex-bold'>(C)</span>\ 1024 \qquad<span class='latex-bold'>(D)</span>\ 1512 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}