For more than 20 years, I posed a monthly unsolved recreational mathematics problem, and posted the solutions I received. You can explore the archive of these problems below, by type of problem or by date. I also gathered some of the more interesting unsolved problems here.
Math Magic Archive
Tiling Reptiles Packing Squares Circles Covering Touching Graphs Numbers Digits Matrices Chess Games Other
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

1998

 

Divisor Chains
(November 1998)

updated 4/23/19

Integer Square Tilings
(December 1998)

updated 10/16/07

1999

Angle Frequencies
(January 1999)

updated 1/28/99

Disconnected Polyominoes
(February 1999)

updated 3/3/99

Average Arrays
(March 1999)

updated 3/7/99

Convex Spectra
(April 1999)

updated 4/13/21

Surround Numbers
(May 1999)

updated 3/5/02

Palindrome Products
(June 1999)

updated 10/12/17

Fairy Chess Endgames
(July 1999)

updated 4/20/01

Rectangles in Squares
(August 1999)

updated 7/9/07

Square Matrices
(September 1999)

updated 10/5/99

Stacking Squares Vertically
(October 1999)

updated 10/10/10

Non-monochromatic Cliques
(November 1999)

updated 11/25/99

Single Digit Formulas
(December 1999)

updated 12/15/02

2000

Bracing Polygons
(January 2000)

updated 10/1/06

Adding Digits Pairwise
(February 2000)

updated 8/27/11

Longest Sokoban Games
(March 2000)

updated 10/24/12

Packing Two Square Sizes
(April 2000)

updated 5/24/15

Counting Domino Tilings
(May 2000)

updated 1/15/05

Problems with L's
(June 2000)

updated 3/14/05

Cayley Graphs of
Sliding Puzzles
(July 2000)

updated 7/22/00

Friedman Numbers
(August 2000)

updated 1/30/20

Covering Squares
(September 2000)

updated 3/29/16

Graphs with
No 4-Cycles
(October 2000)

updated 5/26/03

Variants of Nim
(November 2000)

updated 11/17/08

Power Products
(December 2000)

updated 12/14/00

2001

Packing Two Polyominoes
(January 2001)

updated 2/3/01

Chess Placement and
Sliding Puzzles
(February 2001)

updated 11/18/03

Linear Polyominoes
(March 2001)

updated 10/24/12

Adjacency Graphs
for Polygons
(April 2001)

updated 1/10/21

Getting to Two
(May 2001)

updated 7/1/09

Printer Errors
(June 2001)

updated 2/23/17

Tilings with N Neighbors
(July 2001)

updated 8/12/01

Squaring and Striking
(August 2001)

updated 8/31/01

Counting Square Tilings
(September 2001)

updated 10/9/01

Entangled Polyominoes
(October 2001)

updated 12/21/02

Robot Rooms
(November 2001)

updated 9/6/12

Square Strip Tilings
(December 2001)

updated 7/4/20

2002

Square Crosswords
(January 2002)

updated 1/27/02

Modular Sum Matrices
(February 2002)

updated 1/5/03

Minimal Critical Circuits
(March 2002)

updated 1/6/03

Packing Consecutive L's
(April 2002)

updated 4/30/02

Square Root Approximations
(May 2002)

updated 5/18/02

Diverse Square Tilings
(June 2002)

updated 2/12/13

Fair 2 Game Schedules
(July 2002)

updated 8/9/02

Partridge Packings
(August 2002)

updated 9/12/02

Cellular Growth Model
(September 2002)

updated 9/12/02

Irreptiles
(October 2002)

updated 10/10/18

Sum-Product Matrices
(November 2002)

updated 11/20/02

Consecutive Aspect
Ratio Squares
(December 2002)

updated 12/15/02

2003

Mathematical
Cellular Automata
(January 2003)

updated 6/29/14

Home Plate Tilings
(February 2003)

updated 2/4/13

Triangular Polyhex Tilings
(March 2003)

updated 4/14/03

Efficient Stamps
(April 2003)

updated 6/21/10

Snake Squares
(May 2003)

updated 9/29/20

Multiple Matrices
(June 2003)

updated 6/21/03

Stacking L's
(July 2003)

updated 10/30/11

Squaring and Adding
(August 2003)

updated 8/24/11

Pairwise Touching Polycubes
(September 2003)

updated 9/11/03

Power Towers
(October 2003)

updated 10/26/03

More Square Problems
(November 2003)

updated 10/7/20

Honest Numbers
(December 2003)

updated 1/10/04

2004

Packing Squares
of Area n
(January 2004)

updated 1/8/11

Number Constellations
(February 2004)

updated 3/8/04

Thunderball
(March 2004)

updated 4/5/04

Strobogrammatic
Expressions
(April 2004)

updated 4/23/06

Digit Isogrids
(May 2004)

updated 5/25/04

Packing Aspect
Ratio Rectangles
(June 2004)

updated 6/7/04

Packing Sequences
(July 2004)

updated 6/5/15

Small Digit Approximations
(August 2004)

updated 3/11/19

Polypolyforms
(September 2004)

updated 8/6/08

Repeating Blocks
in Squares
(October 2004)

updated 10/31/04

Galvagni Numbers
(November 2004)

updated 7/20/09

Neighborly Tilings
(December 2004)

updated 6/28/18

2005

Ambiguous Products
(January 2005)

updated 1/31/05

Tiling Rectangles
With U's
(February 2005)

updated 3/29/05

Non-Attacking Bishops
(March 2005)

updated 4/26/05

Areas of Rigid Tents
(April 2005)

updated 4/29/05

Balanced Consecutive Tilings
(May 2005)

updated 6/7/05

Generalized Reptiles
(June 2005)

updated 9/7/15

No-Touch Tilings
(July 2005)

updated 7/30/05

Trivial Knight Tours
(August 2005)

updated 6/7/09

Yet More
Square Problems
(September 2005)

updated 11/12/11

Some Circle Problems
(October 2005)

updated 7/14/07

Shapes Touching
n Others
(November 2005)

updated 11/29/05

Matchstick Graphs
(December 2005)

updated 4/15/17

2006

Sub-Partridge
Rectangle Tilings
(January 2006)

updated 1/31/06

Some Graph Problems
(February 2006)

updated 2/14/06

Playing Card Problems
(March 2006)

updated 7/27/13

Packing Polyominoes
in Larger Copies
(April 2006)

updated 2/17/08

Tiling Triangles,
Pyramids, and Diamonds
(May 2006)

updated 8/30/10

The Tetromino
Placement Game
(June 2006)

updated 6/12/06

Attacking Each
Square n Times
(July 2006)

updated 3/13/07

Polypolylines
(August 2006)

updated 5/11/07

Unique Path Puzzles
(September 2006)

updated 7/31/11

Tree-Like Buildings
(October 2006)

updated 12/3/06

Polyomino Addition
(November 2006)

updated 4/19/09

Polygon Triangulation
(December 2006)

updated 2/24/11

2007

Polyomino Intersections
(January 2007)

updated 1/15/07

Pieces Attacking
Each Other
(February 2007)

updated 3/11/15

Tiling
Cornerless Rectangles
(March 2007)

updated 3/31/07

Chess Attack Loops
(April 2007)

updated 4/22/07

Magic Polyomino Squares
(May 2007)

updated 5/30/07

Anti-Partridge Tilings
(June 2007)

updated 7/2/07

Non-Attacking
Rook Tours
(July 2007)

updated 7/25/07

Stacking Squares Horizontally
(August 2007)

updated 3/25/23

Seeing An Equal
Number of Squares
(September 2007)

updated 3/25/23

The Game Of Blob
(October 2007)

updated 10/28/07

Substring Iteration
(November 2007)

updated 11/13/07

Loops Of Squares
In Rectangles
(December 2007)

updated 6/30/16

2008

Tiling Frames
(January 2008)

updated 2/17/08

Placing Circles To
Obstruct Circles
(February 2008)

updated 3/3/08

Nth Powers
With N Digits
(March 2008)

updated 3/12/08

Packing Pieces
in Polyominoes
(April 2008)

updated 3/24/17

Fitting Inside Two
Different Squares
(May 2008)

updated 12/16/09

Power Problems
(June 2008)

updated 7/29/08

Uniquely Packed Regions
(July 2008)

updated 7/15/08

Number Grids
(August 2008)

updated 8/12/08

Symbiotic Tilings
(September 2008)

updated 11/26/18

Mathematical Anagrams
(October 2008)

updated 6/6/10

Probabilistic Spinners
(November 2008)

updated 11/17/08

Digit Total Graphs
(December 2008)

updated 3/3/11

2009

Chess Pieces and
Polyominoes
(January 2009)

updated 8/10/15

Describing Letters
With Phrases
(February 2009)

updated 1/6/11

Polyomino Letterforms
(March 2009)

updated 3/1/09

Pandigital Factoring
(April 2009)

updated 4/1/09

Rotating Rectangles
in Boxes
(May 2009)

updated 5/22/09

More Tiling Problems
(June 2009)

updated 4/10/16

Weightominoes
(July 2009)

updated 7/31/09

Multiplicative Grids
(August 2009)

updated 8/1/09

Unique Rectangle Packings
(September 2009)

updated 9/26/09

3-Colored Plane Tilings
(October 2009)

updated 2/16/10

The Elevator Problem
(November 2009)

updated 11/13/09

32 + 42 = 52
(December 2009)

updated 12/24/09

2010

Custom Poker Odds
(January 2010)

updated 10/24/12

Spaced Out
Polyomino Tilings
(February 2010)

updated 5/14/10

Packing Two Shapes
(March 2010)

updated 11/5/12

Strata and
Ringed Tilings
(April 2010)

updated 4/20/10

Base Printer Errors
(May 2010)

updated 6/26/10

Packing Circles and
Squares in Rectangles
(June 2010)

updated 2/26/19

Packing Squares in
Circles and Triangles
(July 2010)

updated 7/10/10

More Tiling Problems
(August 2010)

updated 9/16/20

Unique Math Puzzles
(September 2010)

updated 9/25/10

Square Sum Sets
(October 2010)

updated 10/13/10

Counting
Hamiltonian Circuits
(November 2010)

updated 11/8/10

More Polyomino
Chess Problems
(December 2010)

updated 7/21/11

2011

Restricted Square Packing
(January 2011)

updated 10/12/17

2 Player Games
(February 2011)

updated 2/24/11

Integer Circle Packings
(March 2011)

updated 4/1/11

Multi-Latin
Square Packings
(April 2011)

updated 4/17/11

Iterating Two Functions
(May 2011)

updated 5/17/11

Powerful Matrices
(June 2011)

updated 8/6/13

More Chess Problems
(July 2011)

updated 7/15/11

Distinguishing Marks
(August 2011)

updated 8/20/11

Far Away Dice
(September 2011)

updated 9/1/11

Binomial Trivia
(October 2011)

updated 10/1/11

Chess Covering Sets
(November 2011)

updated 11/12/11

Inherited Square Graphs
(December 2011)

updated 4/1/19

2012

Pizza Packing
(January 2012)

updated 1/26/12

Ascending Tilings
(February 2012)

updated 2/10/12

Equal Pieces in
Unequal Containers
(March 2012)

updated 3/21/12

Self-Reproducing
Numbers
(April 2012)

updated 4/28/12

Filling Squares
With Squares
(May 2012)

updated 1/2/16

Unique Digit Equations
(June 2012)

updated 6/1/12

Packing Sliced Squares
(July 2012)

updated 8/15/12

Packing Distinct
Integer-Area Squares
(August 2012)

updated 9/18/12

Eliminating Graphs
(September 2012)

updated 1/5/19

Packing Tuna
and Soup Cans
(October 2012)

updated 10/24/12

Shortest Games
(November 2012)

updated 11/1/12

Weight Puzzles
(December 2012)

updated 12/20/12

2013

Packing k Squares
Each of Areas 1-n
(January 2013)

updated 5/30/17

Triangle Clusters
(February 2013)

updated 2/13/13

Circles Covering
Grid Rectangles
(March 2013)

updated 3/31/13

Repeating
Chess Positions
(April 2013)

updated 4/18/13

Packing Different Digits
(May 2013)

updated 5/20/13

High Hanoi Tilings
(June 2013)

updated 6/27/13

Fractional
Friedman Numbers
(July 2013)

updated 7/26/13

Packing
Overlapping Circles
(August 2013)

updated 8/1/13

Tiling Enlargements
(September 2013)

updated 10/2/13

2-Regular Chess Positions
(October 2013)

updated 12/28/13

Approximating Resistances
(November 2013)

updated 11/30/13

Packing Octagons
(December 2013)

updated 12/1/13

2014

Rigid Packings
of Rectangles
(January 2014)

updated 1/1/14

Increasing and Decreasing
Prime Grids
(February 2014)

updated 2/23/14

Packing Squares
of Area 1 and 2
(March 2014)

updated 3/29/15

Approximating π and e
with ln's and √'s
(April 2014)

updated 4/10/14

Packing a Square with
2 Sizes of Circles
(May 2014)

updated 5/23/14

Faces of Polycubes
(June 2014)

updated 8/2/14

Cubes Filling Cubes
(July 2014)

updated 3/2/15

Rigid Points
Inside a Square
(August 2014)

updated 8/1/14

Equivalent Numerical
Polyominoes
(September 2014)

updated 9/20/14

Smallest Square Overlaps
(October 2014)

updated 10/30/14

Packing Two Sizes
of Triangles
(November 2014)

updated 11/11/14

Tiling Rectangles
with Overlap
(December 2014)

updated 12/1/14

2015

Knight Life
(January 2015)

updated 1/11/15

Attacking a Constant
Number of Vacant Squares
(February 2015)

updated 2/16/15

Touch Cycles
(March 2015)

updated 3/11/15

Packing Hexagons
and Triangles
(April 2015)

updated 4/1/15

Inefficient Greedy Cycles
(May 2015)

updated 5/10/15

Polyomino Barriers
Creating n Paths
(June 2015)

updated 6/1/15

Equal Expressions from
Consecutive Numbers
(July 2015)

updated 7/1/15

Packing Polylines
(August 2015)

updated 8/11/15

Packing Polyominoes
with Squares
(September 2015)

updated 9/16/15

Triangle Strip Tilings
(October 2015)

updated 10/20/15

Power Indices
(November 2015)

updated 11/1/15

Packing Squares
in Two Squares
(December 2015)

updated 12/1/15

2016

Seven Seas
(January 2016)

updated 1/1/16

Short-Move Chess Loops
(February 2016)

updated 2/1/16

Tiling with Numerous
Identical Holes
(March 2016)

updated 3/19/16

Polyform Floes
(April 2016)

updated 4/1/16

Number Names
(May 2016)

updated 5/19/16

Covering a Grid
with Triangles
(June 2016)

updated 6/1/16

Polyominoes Touching
n Times Their Area
(July 2016)

updated 3/25/23

Repeating Flash Cards
(August 2016)

updated 8/26/16

Queens Attacking Vacant
Squares k Times
(September 2016)

updated 9/24/16

Two Types of Polyominoes
Touching Certain Areas
(October 2016)

updated 3/25/23

Packing Two Sizes
Of Hexagons
(November 2016)

updated 11/23/16

Equal Numbers of
Adjacency Numbers
(December 2016)

updated 12/19/16

2017

Langford List
Generalizations
(January 2017)

updated 1/1/17

Triangle Chains
(February 2017)

updated 3/1/17

Decreasing Square Paths
(March 2017)

updated 3/22/17

Tiling Rectangles with
Non-Touching Polyominoes
(April 2017)

updated 4/1/17

Packing Squares
with Polyominoes
(May 2017)

updated 5/15/17

Planar Graphs with
Linear Sums
(June 2017)

updated 6/1/17

Average Lattice Sets
(July 2017)

updated 7/25/17

Neighbor Sets of States
(August 2017)

updated 8/27/17

Packing Squares
Missing Corners
(September 2017)

updated 9/19/17

Sums of Powers Oddities
(October 2017)

updated 10/1/17

Cutting Disks to
Pack Two Disks
(November 2017)

updated 11/19/17

Modeling Political Platforms
(December 2017)

updated 12/1/17

2018

Stick Breaking Probabilities
(January 2018)

updated 1/1/18

Close Prime Signatures
(February 2018)

updated 2/20/18

Primorial Problems
(March 2018)

updated 3/1/18

Packing Digits in Rectangles
(April 2018)

updated 4/26/18

N-ary Circle Trees
(May 2018)

updated 5/1/18

Permutation Polynomials
(June 2018)

updated 6/1/18

Neighborly Squares
(July 2018)

updated 9/29/18

Covering Equal Squares with
Consecutive Squares
(August 2018)

updated 8/1/18

City Substitution Equations
(September 2018)

updated 9/1/18

Sum-Product Polyominoes
(October 2018)

updated 10/1/18

Skyline
(November 2018)

updated 11/23/18

More Polyomino Problems
(December 2018)

updated 12/16/18

2019

Stacking Squares
in Small Boxes
(January 2019)

updated 2/9/19

Packing with
Golden Rectangles
(February 2019)

updated 2/1/19

Variable Mate Problems
(March 2019)

updated 3/17/19

Packing Rigid Polykings
(April 2019)

updated 4/1/19

Specific Touching of
1-, 2-, and 3-ominoes
(May 2019)

updated 6/25/19

Anti-, Shifted-, and Paired
Friedman Numbers
(June 2019)

updated 6/26/19

Multiplication Problems
(July 2019)

updated 7/31/19

Crossing a Pond
(August 2019)

updated 8/26/19

Uniquely Labeled Equal
Sum Planar Graphs
(September 2019)

updated 9/21/19

Square Tilings with
Adjacency Signatures
(October 2019)

updated 10/14/19

Polyomino Tilings with
Adjacency Signatures
(November 2019)

updated 11/1/19

Product-Maximizing Packings
(December 2019)

updated 12/1/19

2020

Packing Circles in Squares
to Avoid Others
(January 2020)

updated 1/15/20

Tournaments to Sort Ability
(February 2020)

updated 2/1/20

Leaky Pitcher Problem
(March 2020)

updated 3/1/20

Packing Squares and Triangles
(April 2020)

updated 4/12/20

Packing Unions of Squares
(May 2020)

updated 5/29/20

Packing Squares
of Sides 1 and 2
(June 2020)

updated 6/1/20

Long Replacement Puzzles
(July 2020)

updated 7/1/20