90 lines
5.7 KiB
HTML
90 lines
5.7 KiB
HTML
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<h2>Look and say sequence</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 419</h3><span style="width:300px;color:#666;">Published on Saturday, 16th March 2013, 10:00 pm; Solved by 257</span></div>
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<p>
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The <b>look and say</b> sequence goes 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...<br />
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The sequence starts with 1 and all other members are obtained by describing the previous member in terms of consecutive digits.<br />
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It helps to do this out loud:<br />
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1 is 'one one' <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 11<br />
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11 is 'two ones' <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 21<br />
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21 is 'one two and one one' <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 1211 <br >
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1211 is 'one one, one two and two ones' <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 111221<br />
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111221 is 'three ones, two twos and one one' <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 312211<br />
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...
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<p>
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Define A(n), B(n) and C(n) as the number of ones, twos and threes in the n'th element of the sequence respectively.<br />
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One can verify that A(40) = 31254, B(40) = 20259 and C(40) = 11625.
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<p>
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Find A(n), B(n) and C(n) for n = 10<sup>12</sup>.<br />
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Give your answer modulo 2<sup>30</sup> and separate your values for A, B and C by a comma.<br />
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E.g. for n = 40 the answer would be 31254,20259,11625
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