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Given a triangle \( \triangle ABC \) with \( \angle A = 20^\circ \), and points \( N \) and \( M \) such that \( AN = MC \) and \( NB = AM \), determine the measure of \( \angle X \).
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30^\circ
| -1
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Mathematics -> Geometry -> Plane Geometry -> Angles
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In a game, there are three piles of balls, each initially containing an equal number of balls. On each turn, you select one pile and transfer a ball to another pile. The score for this move is calculated as the number of balls in the source pile minus the number of balls in the target pile (excluding the ball being transferred). If the result is negative, you lose points. What is the highest possible score you can achieve after making moves for 1000 years?
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\infty
| -1
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Mathematics -> Discrete Mathematics -> Combinatorics
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In a truth table with $n^2$ entries, an algorithm takes two rows, $a$ and $b$, and performs $s$ logical operations, resulting in Boolean values. If each iteration returns $c$ TRUE values, where $c > b - a + 1$, determine the number of additional operations required before selecting a new pair of rows.
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c - (b - a + 1)
| -1
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Mathematics -> Discrete Mathematics -> Logic
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Determine the number of different functions \( f(x) \) that satisfy the given conditions and also have the property that \( f(0) = 1 \).
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1
| -1
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Mathematics -> Algebra -> Abstract Algebra -> Other
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