...in the example below contains <math>9</math> different numbers, as in the first three rows of a Sudoku puzzle.
...row. For the second row, we will consider a little casework. WLOG let the first row be <imath>123 | 456 | 789</imath> (bars indicate between the <imath>3\t
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11 KB (1,749 words) - 23:11, 8 November 2025
...math> <math>k</math> <math>\leq</math> <math>5</math>, at least one of the first <math>k</math> terms of the permutation is greater than <math>k</math>.
If the first number is <math>6</math>, then there are no restrictions. There are <math>5
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11 KB (1,761 words) - 12:13, 24 January 2024
A pseudo-class is normally between a selector and the first curly bracket, always starts with a colon ( : ), and this colon is always i
Note that for :nth-child(1), :first-child is a universally accepted replacement.
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15 KB (2,197 words) - 21:49, 24 July 2023
...15</math> feet. He then measures <math>2</math> feet to either side of the first and last trees in the row before the ends of the yard. Tony uses these meas
people at the first game, then <math>197</math> at the second, <math>203</math> the third, <mat
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71 KB (11,749 words) - 11:39, 20 November 2024
...t the rows could be chosen, but without loss of generality let them be the first three rows. (Change the order of the rows to make this true.) We will mul
...one square in the first two columns shaded. That means that in total, the first two rows have <math>2+5=7</math> squares shaded in- that is false since it
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14 KB (2,337 words) - 19:07, 7 September 2025
...etition from their schools. The state competition is generally held on the first Saturday of March at the Community College of Rhode Island (CCRI), Warwick.
The top 8 compete in an unofficial Countdown round where the first round consists of:
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10 KB (1,309 words) - 18:31, 5 June 2025
For example, in the first iteration, i = 1, so Python prints 1.
All those nested up_down_arrow's might be confusing at first, but it really isn't that confusing.
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37 KB (6,004 words) - 14:57, 18 May 2025
(i) The weakest player chooses the first two contestants.
(iii) The first person to win two games wins the tournament.
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7 KB (1,276 words) - 23:27, 11 November 2025
...ve <math>1</math> or <math>3</math> coins. A coin flip determines who goes first. Whoever removes the last coin wins the game. Assume both players use their
...{(B)}</math> Jenna will win with <math>2013</math> coins, and whoever goes first will win with <math>2014</math> coins.
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5 KB (794 words) - 10:59, 16 July 2024
...is the probability that every even number appears at least once before the first occurrence of an odd number?
...6 of the numbers are even, there is a <math>\frac36</math> chance that the first number we choose is even.
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12 KB (1,900 words) - 22:12, 3 November 2025
...a game goes first in the next game. Suppose that Alfred goes first in the first game, and that the probability that he wins the sixth game is <math>m/n\,</
...f the coin lands heads on an odd numbered flip. So, the probability of the first person winning the game is <math>\frac{1}{2}+\frac{1}{8}+\frac{1}{32}+\cdot
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7 KB (1,058 words) - 19:57, 22 December 2020
...ing cases: the string ends in <math>1, 10,</math> or <math>100</math>. The first case is just <math>M_n</math>. The second case is <math>M_{n-1}</math>. The
...r <math>n - 3.</math> We thus break it up into cases, based on whether the first house gets mail or not.
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15 KB (2,731 words) - 00:38, 1 September 2025
...the first <math>4022</math> terms is <math>380</math>. Find the sum of the first <math>6033</math> terms.
...the first <math>2011</math> terms is <math>200</math>, and the sum of the first <math>4022</math> terms is <math>380</math>, the sum of the second <math>20
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4 KB (633 words) - 23:44, 31 August 2025
...and multiply by <imath>2</imath> (because we can convert each path in the first case to one in the second case by turning <imath>R</imath>'s to <imath>U</i
For <imath>U</imath>, let <imath>a</imath> be the length of the first block of <imath>U</imath>'s and <imath>b</imath> be the second block of <im
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9 KB (1,556 words) - 23:32, 11 November 2025
...t numbers satisfy the property that the middle digit is the average of the first and the last digits?
...st and last digits, twice the middle digit must be equal to the sum of the first and last digits.
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4 KB (690 words) - 16:44, 1 July 2025
First, there are <math>\binom{7}{5}</math> ways to choose the man-woman diameters
Place the first man on the circle. There are 14 ways to do this. Doing this removes two spo
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12 KB (1,943 words) - 09:33, 21 September 2025
...picking the first digit, then the second, and so on until the fourth. The first digit can be any number from one to nine — zero excluded, or else it ceases
...with the sole exception of the previous digit. Regardless of whatever the first digit is, we know that it removes one option, so there are <math>8 - 1 = 7<
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13 KB (2,018 words) - 14:31, 10 January 2025
The first line of the file sets the '''document class''' with the <code>\documentclas
|\topskip || Distance from top of main text box to the baseline of the first line of text in the main text box.
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29 KB (4,929 words) - 12:26, 12 September 2024
Examine the first term in the expression we want to evaluate, <math>\frac{\sin 2x}{\sin 2y}</
=== The First Term ===
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7 KB (1,192 words) - 00:49, 20 September 2025
...d <math>\textit{after}</math> the first <math>1</math> that he rolled. His first <math>31</math> rolls make the sequence <math>4,3,11,3,11,8,5,2,12,9,5,7,11
In general, rolling your first n on roll k is <math>(\frac{11}{12})^{(k-1)} \cdot (\frac{1}{12})</math>.
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3 KB (461 words) - 12:09, 2 January 2020
