Search results

  • Note that this is just the definition for a centered hexagonal number, and the formula for <math>(n-1)^{th}</math> term is <math>3n(n+1)+1</math
    2 KB (268 words) - 06:28, 13 September 2020
  • * [[Hexagonal number]]
    714 bytes (97 words) - 07:29, 9 October 2024
  • ...\angle E,</math> and <math>\angle F</math> are congruent. The area of the hexagonal region is <math>2116(\sqrt{2}+1).</math> Find <math>AB</math>. ...h>\log_{10} n</math>, where <math>n</math> is a positive integer. Find the number of possible values for <math>n</math>.
    8 KB (1,356 words) - 08:38, 2 January 2025
  • ...one can get by discarding <math>100</math> digits, in any order, from the number <math>123456789101112 \dots 585960</math>? ...ural numbers) and <math>c</math> is a five-digit positive integer (natural number)ems/Problem I2|Solution]]
    9 KB (1,449 words) - 19:49, 2 October 2020
  • Cindy was asked by her teacher to subtract <math>3</math> from a certain number and then divide the result by <math>9</math>. Instead, she subtracted <math ...h> MB each. No file can be split between floppy disks. What is the minimal number of floppy disks that will hold all the files?
    12 KB (1,813 words) - 20:39, 19 July 2024
  • ...g the athlete's age, in years, from <math>220</math>. To the nearest whole number, what is the target heart rate of an athlete who is <math>26</math> years o Find the number of two-digit positive integers whose digits total <math>7</math>.
    13 KB (1,860 words) - 14:14, 20 November 2024
  • ...them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different ways can this happen? Note that if <math>n</math> is the number of friends each person has, then <math>n</math> can be any integer from <ma
    6 KB (949 words) - 10:22, 3 November 2024
  • ...squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did ...o the sum of the previous four integers the sum is 57. What is the minimum number of odd integers among the 6 integers?
    18 KB (2,350 words) - 17:48, 9 July 2023
  • A bug travels from A to B along the segments in the hexagonal lattice pictured below. The segments marked with an arrow can be traveled o The number of cases for this is just each vertical set of arrows multiplied to each ot
    16 KB (1,622 words) - 21:00, 17 July 2024
  • ...squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did ...to the sum of the previous 4 integers, the sum is 57. What is the minimum number of even integers among the 6 integers?
    20 KB (2,685 words) - 16:12, 10 November 2024
  • ...ll be the difference between the total number of white tiles and the total number of black tiles in the new figure?
    1 KB (215 words) - 19:20, 12 October 2020
  • A nickel is placed on a table. The number of nickels which can be placed around it, each tangent to it and to two oth Arranging the nickels in a hexagonal fashion, we see that only <math>\boxed{\textbf{(C) }6}</math> nickels can b
    540 bytes (82 words) - 16:13, 14 March 2023
  • Let <math>S</math> be the number of ordered pairs of integers <math>(a,b)</math> with <math>1 \leq a \leq 10 The number <math>n</math> can be written in base <math>14</math> as <math>\underline{a
    8 KB (1,284 words) - 13:35, 9 August 2021
  • ...th>3</math> of the <math>12</math> vertices determine a triangle. Find the number of these triangles that are isosceles (including equilateral triangles). ...th>2 \cdot 12 = 24</math> for four ways to put the third point. Adding the number up, the final answer is <math>24+28 = \boxed{052}.</math>
    6 KB (1,023 words) - 09:38, 21 November 2023
  • ...> are placed in the following <math>6</math> tokens that are arranged in a hexagonal order. The pairwise products of all opposite tokens are all equal. Some num The niceness of a positive number <math>n</math> with divisors <math>1=d_1<d_2<d_3<\dots<d_k=n</math> is equa
    14 KB (2,267 words) - 11:49, 9 June 2020
  • ...> are placed in the following <math>6</math> tokens that are arranged in a hexagonal order. The pairwise products of all opposite tokens are all equal. Some num <math>u = a + bi</math> is a complex number such that <cmath>(2+i)^2 u^2 = 50i. </cmath> What is the positive value of
    15 KB (2,388 words) - 12:24, 9 June 2020
  • What is the least possible denominator of a positive rational number whose using $13.60? Express your answer as a mixed number.
    11 KB (1,672 words) - 20:18, 12 March 2023
  • ...gular hexagonal blocks of side length 1 unit are arranged inside a regular hexagonal frame. Each block lies along an inside edge of the frame and is aligned wit The number <math>\frac{3}{7}</math> is irrelevant to solve the problem.
    13 KB (1,944 words) - 01:20, 11 November 2024
  • ...th> For how many dates in <math>2023</math> does each digit appear an even number of times in the <math>8</math>-digital display for that date? * The number <math>N</math> is divisible by <math>7</math>.
    16 KB (2,411 words) - 17:04, 23 November 2024