Seems some of us can't see a problem without wanting to take a crack at solving it. Does that sound like you?
Good. Forge ahead and ponder this month's problem. We'll post a new one every month, and allow a month for you to submit solutions (we may even publish submitted answers, especially if they're correct).
And now... here's our
Oct. 2024 challenge!
Here is the solution for our August 2024 problem
We usually won't reply individually to submitted solutions but every few days we will update a list of people who answered correctly. At the beginning of the next month, we'll post the answer.
So give your mind a break from its routineyou never know what other problems you may solve in the process!
Hosted by
IBM Research  Israel
The current puzzlemaster of Ponder This is Gadi Aleksandrowicz. Previous puzzlemasters include Oded Margalit (20072020), James Shearer (20052009), and Don Coppersmith (19982005).
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If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com
Ponder This Top 52 SolversList Updated: June 20th 2024
Solver  Challenges solved 

Daniel Bitin  188 
Dan Dima  169 
David Greer  144 
RaduAlexandru Todor  133 
Clive Tong  129 
Motty Porat  127 
Joseph DeVincentis  118 
Nyles Heise  115 
Todd Will  112 
Daniel Chong Jyh Tar  105 
Andreas Stiller  104 
Lorenz Reichel  103 
Liubing Yu  102 
Kang Jin Cho  102 
Amos Guler  99 
Chris Shannon  99 
Reiner Martin  96 
Tamir Ganor  95 
David Friedman  92 
Dieter Beckerle  92 
Shouky Dan  91 
Bert Dobbelaere  89 
John Tromp  87 
Albert Stadler  87 
Alper Halbutogullari  86 
Florian Fischer  82 
Solver  Challenges solved 

Armin Krauss  81 
Victor Chang  78 
Gary M. Gerken  76 
James Dow Allen  76 
Alex Fleischer  76 
Vladimir Volevich  76 
Harald Bögeholz  74 
Li Li  73 
Chuck Carroll  72 
Shirish Chinchalkar  71 
Graham Hemsley  71 
Mathias Schenker  66 
Peter Gerritson  65 
Bertram Felgenhauer  64 
Uoti Urpala  63 
Oscar Volpatti  61 
Michael Liepelt  60 
Marco Bellocchi  59 
Arthur Vause  58 
Luke Pebody  56 
Michael Brand  55 
John G. Fletcher  54 
David F.H. Dunkley  53 
Dominik Reichl  53 
Latchezar Christov  53 
Franciraldo Cavalcante  50 
Archive

2024
October 2024: # Splitting a number
September 2024: # Sibling triangles
August 2024: # Playing blind the setmatching game
July 2024: # Tiling with balanced black and white tiles
June 2024: # Pythagorean triple approximations to pi
May 2024: # Possible Dobble decks
April 2024: # Simultaneous Towers of Hanoi
March 2024: # Composite Sequences
February 2024: A Dice Game
January 2024: A child's set of equations

Previous Years

2023
December 2023: Circles on a triangular grid
November 2023: The 15 Puzzle and magic squares
October 2023: Nonpalindromic numbers with palindromic squares
September 2023: Prime Number Generation using GCD
August 2023: Squaretriangular numbers
July 2023: Sliding Pieces Game
June 2023: The temporal cheese maze
May 2023: Computing quadratic forms
April 2023: Lightbulb grid game
March 2023: Chained Primes
February 2023: The queens and kings problem
January 2023: Gene editing

2022
December 2022: Unique Solution Letter Boxed
November 2022: The sock drawer
October 2022: Numbers in a cube
September 2022: Symmetric ISRL shape
August 2022: Safety dance
July 2022: The cell doubling game
June 2022: Counting odd polyominoes
May 2022: Splitting a set in two for sum 0
April 2022: Minimizing a sum for two orthogonal vectors
March 2022: Primle
February 2022: Representation of numbers using powers of 2 and 3
January 2022: Forming primes in digit circles

2021
December 2021: Galton Board
November 2021: Sliding maze puzzle  part 2
October 2021: Sliding maze puzzle
September 2021: Superhero team sequencing
August 2021: Coin Toss Battle Royale
July 2021: Square roots of unity modulo Carmichael numbers
June 2021: Primes that are sums of powers
May 2021: Fibonaccilike sequence with no primes
April 2021: Decremental wheel of choice
March 2021: Perseverance rover
February 2021: The trusted neighbors' vaccination ring
January 2021: Vaccinating Robot

2020
December 2020: Maximal losing vote
November 2020: The power game
October 2020: Controlflow graphs
September 2020: Generalized Rock Paper Scissors
August 2020: Tweaking the "Nim" game
July 2020: Sequences generated by letters
June 2020: Farewell and welcome to Gadi Aleksandrowicz!
May 2020: Conway's Game of Life
April 2020: COVID19 outbreak
March 2020: Dicdacdoe
February 2020: Snakes and Ladders
January 2020: 2 poisonous barrels

2019
December 2019: Approximating absolute value
November 2019: Large 9x9 determinant
October 2019: Five banknotes II
September 2019: Five banknote denominations
August 2019: Three restricted permutations cannot cover
July 2019: Large and smallarea knight's cycles
June 2019: Two close sums of the square root of smooth numbers
May 2019: Longest boat trip
April 2019: Prime magic square
March 2019: Rational approximation of square root
February 2019: Debater's score
January 2019: Charlie helps Bob defeat Alice

2018
December 2018: Two circles multiplication create a square
November 2018: 10choose5 short string
October 2018: Different area triangles
September 2018: Monogender in threeletter words
August 2018: (Almost) prime water sharing
July 2018: Aging obscure triplets
June 2018: Five L/J Tetrominoes
May 2018: Two fake coins
April 2018: 9 Balloons
March 2018: Alice and Bob and Six Switches
February 2018: 3 people throw dice
January 2018: Fake news spread

2017
December 2017: Quad9 six degrees of separation
November 2017: A die and two coins
October 2017: IBM security polynomial
September 2017: Fischer’s Fool’s Mate
August 2017: Billiard
July 2017: Zeros in sin(PONDER)*sin(THIS)
June 2017: Math exercise to 100
May 2017: Letter gaps
April 2017: Factoring
March 2017: Eight octopuses with watches
February 2017: How many Boolean sequences
January 2017: Rational solutions for x**y=y**x

2016
December 2016: Fair rope pulling
November 2016: Game of 12 months chefs
October 2016: The best fivedigit number
September 2016: Seating four people for 24 hours
August 2016: Finding bags of counterfeit coins
July 2016: Pentominos tiling (Golomb)
June 2016: Tilting a truncated icosahedron
May 2016: Attacking chess pieces
April 2016: RoboCats falling by cubic polynomial
March 2016: Squareversed numbers
February 2016: IBM InterConnect
January 2016: Efficient bicycle gears

2015
December 2015: EBCDIC to ASCII conversion
November 2015: Watson verbal arithmetic
October 2015: Counting 12 bits using 5to2 functions
September 2015: Awarding N people with 8 multiperson teams
August 2015: Loopsless projections of a loop
July 2015: Four people with 16 hats
June 2015: Drifting complex anomaly detection
May 2015: 3 people betting game
April 2015: 7x7x7 with as much Peters
March 2015: Punched (twice) tape
February 2015: Kakuro  hard version
January 2015: Kakuro  easy version

2014
December 2014: A matrix with 29 solutions
November 2014: Distribution using two coins
October 2014: Last digits of 2^3^4^5^6^7^8^9
September 2014: 2^3^4^5 leading digit on base e
August 2014: Biased binary search
July 2014: Pebbles game on a tetrahedron
June 2014: 25 intersecting Cubes
May 2014: Annihilation probability of 1D gun
April 2014: 1D version of the 2048 game
March 2014: Toggling lamps
February 2014: Juxtaposing a 4D pyramids
January 2014: Boolean 21x6 matrix

2013
December 2013: Gifts graph
November 2013: Kdim faces of ddim hypercube
October 2013: B&W coloring of a chess board
September 2013: Bob and Alice vs the casino
August 2013: Letters on a 9D hypercube
July 2013: Octahedronial dice
June 2013: Find a fraction
May 2013: Computing a polynomial
April 2013: Sum of fractions
March 2013: Buying 5 products
February 2013: Concatenating squares
January 2013: 13 permutation on 18 letters

2012
December 2012: Maximal sum 6x6 grid
November 2012: Lattice of trees blocks light
October 2012: Disdyakis Triacontahedrons dice
September 2012: Parking game
August 2012: 3 charges that almost cancel out
July 2012: Coloring balls games
June 2012: Dividing 1,506,009,006,001,500,000,000
May 2012: Permutation scheduling
April 2012: Garden hose model
March 2012: Balanced binary tree
February 2012: Biased coin game
January 2012: Exploding dragon egg

2011
December 2011: Infinite chess game
November 2011: Volleyball tournament
October 2011: Interesting resistors network
September 2011: Bits to dice and back
August 2011: Triangle area / perimeter
July 2011: School lunches
June 2011: Parking density
May 2011: Distance between bad bars
April 2011: How many snakes
March 2011: Locating faulty bits
February 2011: Flippable number
January 2011: Letters and beans game

2010
December 2010: Counting votes from percentage
November 2010: In honor of Benoit Mandelbrot
October 2010: Finding the size of a pentagon
September 2010: Threaded robot looks for a line
August 2010: Lilliput unique ID numbers
July 2010: 1,000,000,000 divides round((1+2cos(20))**n)
June 2010: A bug in a Boolean circuit
May 2010: Quantization of probability vector
April 2010: Hex = dec, removing last 21 digits
March 2010: Spell names by passing phones
February 2010: 5 moves chess game
January 2010: Make a 5 from 2 and 2

2009
December 2009: Finding 25 bits number using masks
November 2009: Fastest way to find the smallest divisor
October 2009: Complete the sequence
September 2009: Non repeating cumulative sum
August 2009: Implement 3 nots using only 2
July 2009: Ending a backgammon game with a double
June 2009: Value of expression regarding permutation
May 2009: Palindrome time
April 2009: 5ops implementation of erasure code
March 2009: Hexadecimal exercise
February 2009: Find a bug in this unknown riddle
January 2009: Value of a replaceable lottery ticket

2008
December 2008: Probability of random walk tetrominoes
November 2008: Ponder^this = ponder...
October 2008: Jumping frog
September 2008: Partitioning 13x13 to squares
August 2008: Variation on the 8queen problem
July 2008: Covering pentominoes by polyominos
June 2008: Probability of DNA testing
May 2008: Game of life  backwards
April 2008: Polygons formed from squares / triangles
March 2008: How much to bid?
February 2008: What are the rules of the game?
January 2008: Buying random balls out of an urn

2007
December 2007: Finding intermittently failing parts
November 2007: Revealing sets of lights
October 2007: Resistance of Platonic solids
September 2007: Bundle deal of cable TV
August 2007: Describe the sequence
July 2007: Minimum length of blocking fence
June 2007: Sum of random (0,1) game
May 2007: Largest square in a cube
April 2007: Random walk of a frog
March 2007: Shooter / target game
February 2007: When to discard a random number?
January 2007: Future contracts  how many to buy?

2006
December 2006: Cycles size in random permutation
November 2006: Expressions with 1,2,3,4
October 2006: Fraction of area of triangle
September 2006: f(n)=(1+(n*nn)*f(n1))/(n*n+1)
August 2006: Value of future contract
July 2006: Approximations of 1/x and sqrt(x)
June 2006: Fraction of vertical dominoes
May 2006: Distance configuration of 4 points
April 2006: Random walk on a hypercube
March 2006: Expected area of random triangle
February 2006: Random [0,1] poker game
January 2006: Size of smallest/largest piece

2005
December 2005: Barring polyominoes from infinite board
November 2005: Size of finite random binary tree
October 2005: Matrices with special 2x2 minors
September 2005: Acceleration rate of pulley system
August 2005: first N digits of M is divisible by N
July 2005: Covering table with coins
June 2005: Almost balanced A/B strings
May 2005: Rectangular grid / glass cubes
April 2005: Divisibility of integer powers
March 2005: 6x6x6 cube with different signatures
February 2005: Infinite right triangles
January 2005: 7colored 35 beads necklace

2004
December 2004: Projecting points onto the complex plane
November 2004: Sum of numbers after worm ate some
October 2004: GCD of values of primitive polynomial
September 2004: Another versions of turntable
August 2004: Longest way to come home
July 2004: N cups on a turntable
June 2004: Rectangles in the unit square
May 2004: A twist on "Towers of Hanoi" puzzle
April 2004: Labeling VCR cassettes using digit stickers
March 2004: Number of weakly monotone arrays
February 2004: Right isosceles triangle with integer sides
January 2004: Finding duplicates in readonly array

2003
December 2003: Similar dissection of quadrilaterals
November 2003: Line intersecting curve in a pentagon
October 2003: Non attacking new chess pieces II
September 2003: Irrational root of polynomial
August 2003: Non attacking chess pieces
July 2003: Coloring roads to enable blind direction
June 2003: Partitioning a square into rectangles
May 2003: sqrt(1+2*sqrt(1+3*sqrt(...+n*sqrt(1]
April 2003: Bounds on a Hamiltonian tour
March 2003: Fencing a pasture
February 2003: Zero sum in Boolean cards
January 2003: 4 points with odd integer distances

2002
December 2002: 4 integers with squares sums
November 2002: 4 bottles on a square turntable
October 2002: Tournament of N with <=M players
September 2002: Closed subsets of boolean operators
August 2002: Drawing 4D hypercube on a grid
July 2002: 23 prisoners and a switch room
June 2002: Coin weighing using scale
May 2002: Circle passing via 7 lattice points
April 2002: Lifetime of adjacent differences
March 2002: Coffe or tea majority club
February 2002: Undirected graph of diameter 2
January 2002: Gambling casino

2001
December 2001: Knight's tour on 4xN chess boards
November 2001: PB&J asymmetry bounds
October 2001: f maps any open interval onto R
September 2001: Bounds on a permutation group
August 2001: Points on a plane
July 2001: 1/1 + 2/(2+3) + 3/(4+5+6) + ...
June 2001: Goblin chase in a train
May 2001: Goblin chase in a pool
April 2001: College saving account
March 2001: Golf  hit in one
February 2001: Kubricia's 2001 money boxes
January 2001: Counting segments overlays

2000
December 2000: Commuter gets 20 minutes earlier
November 2000: 75 integers in [1,230]
October 2000: One+five(four) cards trick
September 2000: Simplify sqrt expression
August 2000: Six Card Cribbage
July 2000: 2dimensional grid jumping coins
June 2000: Coins game (6.78$)
May 2000: Northwest to the north pole
April 2000: Revamp the tax code
March 2000: Sum of two squares
February 2000: N**C is integer
January 2000: Catching baseball

1999
December 1999: Zeroless multiply of 2**1999
November 1999: Cutting a cube into a box
October 1999: Path 1 or 2 in directed graph
September 1999: Recognizing dishes
August 1999: Seating people on N+M tables
July 1999: Labeling bowling pins
June 1999: 1 plus 1/7 of the medals
May 1999: Integer side rectangles partition
April 1999: Wally's Rock Permuting (WRP)
March 1999: Cliques of people in a ballroom
February 1999: A leashed sheep eats grass
January 1999: Water glass center of mass

1998
December 1998: Removing snow
November 1998: Cutting frosted cake
October 1998: Sorting pancakes
September 1998: Magic Star of David
August 1998: Equilateral triangle
July 1998: Tennis balls in a bucket
June 1998: Shaking hands in a party
May 1998: A belt around the earth

2023