Random Bulgarian solitaire

We consider a stochastic variant of the game of Bulgarian solitaire [M. Gardner (1983), Sci. Amer. 249, 12-21]. For the stationary measure of the random Bulgarian solitaire, we prove that most of its mass is concentrated on (roughly) triangular configurations of certain type.Comment: 28 pages, 4 figures; revised version - to appear in Random Structures and Algorithm

Solving Bulgarian Solitare

Poopćenje Bugarskog solitera je problem pronalaska svih poredaka brojeva koji se dogode dok poredak ne bude konačan za trokutaste brojeve ili dok se poredak ne ponovi. Mnogi matematički problemi se mogu reducirati na problem Bugarskog solitera. Istraženo je rješenje koje heurstičkim pristupom rješava problem. Prikazan je postupak optimalnog rješavanja poopćenog problema Bugarskog solitera algoritmom. Algoritam je implementiran u Pythonu. Rezultati izvršavanja algoritma su analizirani i uspoređeni, te je pokazana vremenska i prostorna složenost za algoritam koji rješava Bugarski soliter.Generalization of Bulgarian solitaire is problem of finding every position of number that occur while position is not in the stable position for triangular number or until position is not repeated. Many mathematical problems can be reduced by Bulgarian solitaire. Solution that use heuristics to solve problem are researched. Procedure of optimal solving generalized Bulgarian solitaire using algorithm is shown. Algorithm are implemented in Python. Results of execution algorithm are analyzed and compared, time and space complexity for algorithm are shown

Solving Bulgarian Solitare

Poopćenje Bugarskog solitera je problem pronalaska svih poredaka brojeva koji se dogode dok poredak ne bude konačan za trokutaste brojeve ili dok se poredak ne ponovi. Mnogi matematički problemi se mogu reducirati na problem Bugarskog solitera. Istraženo je rješenje koje heurstičkim pristupom rješava problem. Prikazan je postupak optimalnog rješavanja poopćenog problema Bugarskog solitera algoritmom. Algoritam je implementiran u Pythonu. Rezultati izvršavanja algoritma su analizirani i uspoređeni, te je pokazana vremenska i prostorna složenost za algoritam koji rješava Bugarski soliter.Generalization of Bulgarian solitaire is problem of finding every position of number that occur while position is not in the stable position for triangular number or until position is not repeated. Many mathematical problems can be reduced by Bulgarian solitaire. Solution that use heuristics to solve problem are researched. Procedure of optimal solving generalized Bulgarian solitaire using algorithm is shown. Algorithm are implemented in Python. Results of execution algorithm are analyzed and compared, time and space complexity for algorithm are shown

Kickshaws

Readers are encouraged to send their own favorite linguistic kickshaws to the Associate Editor. All answers appear in the Answers and Solutions at the end of this issue

Opera Mundi: a weekly report on the economy of the Common Market. No. 360, May 30 - June 5, 1966.

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