82 lines
5.2 KiB
HTML
82 lines
5.2 KiB
HTML
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<h2>Reachable Numbers</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 259</h3><span style="width:300px;color:#666;">Published on Saturday, 10th October 2009, 01:00 pm; Solved by 840</span></div>
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<p>A positive integer will be called <i>reachable</i> if it can result from an arithmetic expression obeying the following rules:</p>
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<ul>
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<li>Uses the digits 1 through 9, in that order and exactly once each.</li>
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<li>Any successive digits can be concatenated (for example, using the digits 2, 3 and 4 we obtain the number 234).</li>
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<li>Only the four usual binary arithmetic operations (addition, subtraction, multiplication and division) are allowed.</li>
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<li>Each operation can be used any number of times, or not at all.</li>
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<li><dfn title='A minus sign applied to a single operand (as opposed to a subtraction operator between two operands)'>Unary minus</dfn> is not allowed.</li>
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<li>Any number of (possibly nested) parentheses may be used to define the order of operations.</li>
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<p>For example, 42 is reachable, since (1/23) * ((4*5)-6) * (78-9) = 42.</p>
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<p>What is the sum of all positive reachable integers?</p>
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