Torsten Sillke

That's me in small.
List of publications and CV
equal surnames in Germany
Address: Ferdinand-Scholling-Ring 30, D-65934 Frankfurt/Main, Germany
Where I am working for: LH Systems.

Problems

• Mathematical Problems - List of several open problems
• Stable sets - The most wanted problem

Results

• Results in Tiling and Packing - polycube and polysphere packings
• Martin Gardner - Contents of his books.

Some Puzzles

Operations Research Puzzles

• Crossing the bridge - with a lamp (Crossing the bridge (long))
• discrete optimization - and a C program

Logic Puzzles

• Sum Product - The impossible Puzzle
• Logic Puzzle - How old are they?
• lias and truth tellers - who is the spy?
• power 10 - powers in first order logic, a Gödel problem
• Mastermind - Errate die Kombination (German)

Probability Puzzles

• expectation - number of fixpoint of a random permutation
• Random cyclic polygons - expected number of points which contain the center
• expectation - number of occurences of a fixed pattern in a 0-1-matrix (Truchet-tile)
• Partition Probabilities - Probability of a Factor (CRUX 2000)
• Red Black Game - How Often Should You Beat Your Kids
• Occupation - Likelihood Approximation
• expectation - Problem collection using Linearity
• Waiting time - poisson process
• 3 Door - Monty Hall puzzle
• Birthday problems - generalization and approximation

Counting Puzzles

• sequences - Sequence Puzzles
• missing number - unusual sequence puzzles
• Elevator sequence
• Triangle Counting - in an regular n-gon
• Triangle Counting - in a triangular grid
• Square Counting - in a square grid
• Sum of reciprocal Binomials
• mod-2 Pascal Triangle - rational generating function
• Domino Tilings - and rhombic tilings.
• Nikolaus - how many Euler paths? (Nikolaus German)
• Euler numbers - Kellogg's problem
• Counting F - read this sentence
• Trinomials - number of odd values
• Divisible strings - consecutive divisible strings (ruby program)
• Triangles - how many triangles can you see?

Decypher

• Alphametics - and Cryptarithms and the pharmacist's code
• Cryptogram - letter substitutions
• Number Place - puzzles
• 3 Digits - puzzles
• Snap - the snap games (spoiler)
• koray's cypher - with hints (German)
• Logical square - what is the missing value?

Puzzle Links

• www.mathpuzzle.com - site of Ed Pegg Jr.
• Problem Corner Org - 20000 math problems
• Erich's Site - Math Magic, Packing Center
• www.puzzles.com - Serhiy Grabarchuk maintains a collection of traditional and original puzzles
• Nick's Mathematical Puzzles - Nick Hobson has a nice collection of mathematical puzzles
• Cut the Knot - interactive mathematics with Alex Bogomolny
• Polyomino Tilings - Micheal Reid's packings of like Polyomonoes
• Polyform Tilings - Andrew Clarke's wonderful site with good graphic and information
• Atlantis - Puzzles, Games and Art - Karl Scherer's site with chess and math puzzles
• Click Mazes - online mazes
• Logic Mazes - Abbott's page
• The Geometry Junkyard - mathematical oriented stuff by David Eppstein.
• Puzzles Archive - rec.puzzles (my local 1993 copy)

German Puzzle Links

• Math 4 u - geometric and inequality problems (German)
• Jürgen Köller's Mathematische Basteleien - (English and German)

Math. Puzzle Magazines

• Quantum - a math magazine (database) with a monthly contest problem
• Mathematics Magazine - a math magazine (database)
• Crux Mathematicorum - problems from mathematical olympiads
• Wurzel - a math. magazine for undergraduate students (German)
• Monoid - a math. magazine of the Univ. Mainz for young persons (German)

Arithmetical and Analytical Puzzles

• Rope around the Earth - pull it tight
• Sunrise - Arnold's eureka
• Speed - Murder on the river
• Speed up - bicycle tour
• x^y = y^x - commuting powers
• Ladder - move a ladder around a corner
• Ladder and Box - ladder on the wall
• hinged Ladder - distance problem
• Define a Function - use min and max
• tripe vector product identity - fight for the best solution
• cube roots - which term is smaller?
• The Crease - Fold a sheet of paper
• 3,4,5 Triangle - halve it
• high percentages - percentage points (English/German)
• harmonic numbers - some questions
• tan sum - a trigonometric identity
• Ages - Who's Birthday?
• Approximation - by two constants
• Cogito: Der Heuhaufen - Wie lange reicht das Heu? (German)
• Alter - Wie alt ist Klaus? (German)

Floor and Ceiling Puzzles

• Sturmian Words - characteristic of a real number
• Floor Sums - equations and inequalities
• Floor Equation - solving equations in real numbers
• Floor Cubed - Concrete Mathematics Club Casino
• Floor Recurrences - recurrences
• Floor Sequences - properties of these sequences
• Floor Integral - integration problems
• Operator - with floors

Whole Number Puzzles

• Magic Hexagon - musings about magic hexagons.
• A Unique Magic Hexagon - Trigg's article
• arithmetic - puzzle, sum of consecutive numbers
• Square Problems - impossible squares
• N Card Monte - probability of picking a pair of the same color
• Engel Problem - integral (a^2+b^2) / (1+ab) are squares
• Prime Problem - proof :-)
• Impossible Polynomial - Diophatic
• 8 squares - Hurwitz equation and solution as ps-file or solution as pdf-file by H. Postl.
• Symmetric Diophatic - 3 vars
• 3 powers - Diophatic
• prime pattern - no universal pattern
• reducing to one digit - casting zeros

Mechanical Puzzles - Jumping, Moving, Sliding Puzzles

• Tails Up - turning 4 coins
• Contact Slide - slide 4 coins into the middle
• Sliding Pennies - Double contact moves
• Leolei - a sliding puzzles with L-pieces
• Peg Solitaire - the cross with different long arms
• Peg Solitaire - program
• Peg Solitaire - WWW Link
• Rubic Cube and beyond - for Cube Lovers (old short info)
• Jumping off of a swing - jump as far as you can

Packing, Covering and Dissecting

• Equilateral Triangle - six piece disscetion
• Pizza Theorem - dissceting a disc. Pizza Dissection with cinderella.
• 3 Square Covering - Minimal Cover of a Square
• Squares Covering a Square - total square area is fixed
• 3 Squares in a circle - a french toast puzzle
• isosceles triangles - a square dissection
• packing - the fridge
• Squares and a Circle - the circle always fits
• Circle in a long rectangle - 2n+1 circles (diameter 1) in a 2*n rectangle
• Four T Puzzle - fit them into a small square. Four T arrangments as a postscript file (8K, 13p)
• Strip Covering - Strip Cover of a Circle
• tilings - topologically equivalent. Solution to Collatz's tiling as a postscript file (111K, 12p). A survey paper of Olaf (in German) on this subject as postscript gzip file (345K, 17p) gives further references and more theory and pictures.
• Fault Free - domino tilings
• dissection - of rectangeles into two parts
• three like discs - a postscript file (1.7 K)
• Lege-Wege - A domino tiling game
• rep-tiles - L shape pieces
• Antislide - rigid domino rectangles
• Langford's Problem - 312132, 23421314 (Miller's Page)
• Wood Puzzles - Two impossible 4 piece puzzles

Geometric Puzzles

• Geometrical Paradox - Where does the hole come from
• Tetraedron Octahedron - some questions
• Trisection - of a line
• Views - reconstruct objects
• Match - some matchsticks
• Regeular Heptagon - four points on a circle
• Three Lines - contruct an equilateral triangle
• Steiner Lehmus - equal angle bisector and isosceles triangles
• van Aubel - squares on a quadrilateral
• circle intersection - a Helly property
• Egg Curves - how to draw eggs
• Spirals

Topological Puzzles

• Magic Pencil - the buttonhole puzzles
• strange painting - hanging on two nails

Information Puzzles

• Gossip - how many phone calls? gossip solutions
• Waiting - for information (common sense information)
• three switches - finding the lost bit
• weighting - six weights 1, 2, 3, 4, 5, 6
• triple weighting - The Eleven Ball Puzzle

Mathematical Competitions

• IMO - official IMO site (links to national Mathematical Olympiads)
• Math Puzzle Competitions - John Scholes' IMO, Putnam, Swiss competitions
• Mathematik-Olympiaden e.V. - German mathematical competitions
• Quantum - a monthly math puzzle problem (with lovely animated pictures)
• The Art of Problem Solving - for eager math students
• Zahlenjagd - a monthly math puzzle problem (German). Very well done.

Puzzle Contest

• Pentacube Contests - figures of old contests

Combinatorial Puzzles

• Cube 3 - No 3 on a line, No 4 on a plane
• Max Integer Set - no pair with distance 3
• Supper Problems - relative prime or division free
• Chain Links - to pay for room
• Some Sum Signs - matrix row and column sums
• Antimagic Matrices - made from -1, 0, 1
• Absolute Difference Triangles - Pool-Ball Tiangles
• Licence Plates - maximal number
• Crossless Matching - in the plane
• Condom Problem - Design
• Many Stars - Arrangement
• Brothers in Law - mutual relations
• Euler Tours - pathes in a grid
• Colored queens - Little queens puzzle
• Word Problem - a free group relation (polyomino)
• algorithm - cyclic word recognition

Algebra Puzzles

• group puzzle - xxx = 1 means xy = yx ?
• ring puzzle - xxx = x means xy = yx (Jacobson problem, a Herstein puzzle)

Lateral Thinking Puzzles

• Situation Puzzles - lateral thinking puzzles website www.lateralpuzzles.com
• Situation Puzzles - Jed's List of Situation Puzzles
• 5 Eier im Korb - wie geht das? (German)

Other Puzzles

• even * even = odd - how can that be?
• dot connection - with straight lines
• word play - word puzzles english and german
• geographicals - Some geographical math questions
• Mnemonics - of Pi
• Riddles - Brain Benders

Algorithms

• Algorithms in C or C++ to use
• Check Codes

Games and Fun

• Twister - my fan page.
• String Figures - oder "anbändeln"

Fakultät für Mathematik | Universität Bielefeld

last changed 2018-12-01