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  2. Kruskal count - Wikipedia

    en.wikipedia.org/wiki/Kruskal_count

    Besides uses as a card trick, the underlying phenomenon has applications in cryptography, code breaking, software tamper protection, code self-synchronization, control-flow resynchronization, design of variable-length codes and variable-length instruction sets, web navigation, object alignment, and others.

  3. Missing square puzzle - Wikipedia

    en.wikipedia.org/wiki/Missing_square_puzzle

    The apparent triangles formed from the figures are 13 units wide and 5 units tall, so it appears that the area should be S = ⁠ 13×5 / 2 ⁠ = 32.5 units. However, the blue triangle has a ratio of 5:2 (=2.5), while the red triangle has the ratio 8:3 (≈2.667), so the apparent combined hypotenuse in each figure is actually bent.

  4. Triangular number - Wikipedia

    en.wikipedia.org/wiki/Triangular_number

    A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number , other examples being square numbers and cube numbers . The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural ...

  5. Triangular array - Wikipedia

    en.wikipedia.org/wiki/Triangular_array

    The Bell triangle, whose numbers count the partitions of a set in which a given element is the largest singleton [1] Catalan's triangle, which counts strings of matched parentheses [2] Euler's triangle, which counts permutations with a given number of ascents [3] Floyd's triangle, whose entries are all of the integers in order [4]

  6. Magic triangle (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Magic_triangle_(mathematics)

    A magic triangle or perimeter magic triangle [1] is an arrangement of the integers from 1 to n on the sides of a triangle with the same number of integers on each side, called the order of the triangle, so that the sum of integers on each side is a constant, the magic sum of the triangle.

  7. Shut the box - Wikipedia

    en.wikipedia.org/wiki/Shut_the_box

    Shut the box (also called ACKPOT, [1] batten down the hatches [1] or trick-track [2]) is a game of dice for one or more players, commonly played in a group of two to four for stakes. Traditionally, a counting box is used with tiles numbered 1 to 9 where each can be covered with a hinged or sliding mechanism, though the game can be played with ...

  8. Burnside's lemma - Wikipedia

    en.wikipedia.org/wiki/Burnside's_lemma

    Burnside's lemma can compute the number of rotationally distinct colourings of the faces of a cube using three colours.. Let X be the set of 3 6 possible face color combinations that can be applied to a fixed cube, and let the rotation group G of the cube act on X by moving the colored faces: two colorings in X belong to the same orbit precisely when one is a rotation of the other.

  9. Triangulation - Wikipedia

    en.wikipedia.org/wiki/Triangulation

    One of the sensors is typically a digital camera device, and the other one can also be a camera or a light projector. The projection centers of the sensors and the considered point on the object's surface define a (spatial) triangle. Within this triangle, the distance between the sensors is the base b and must be known. By determining the ...