## Welcome to our monthly puzzles

You are cordially invited to match wits with some of the best minds in IBM Research.

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). 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 routine---you never know what other problems you may solve in the process!

The current puzzlemaster is Oded Margalit. He took over from James B. Shearer, who took over from the original puzzlemaster Don Coppersmith, in October 2005.

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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

## Archive

### October 2016: The best five-digit number

Challenge Solution

### 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

### December 2015: EBCDIC to ASCII conversion

### November 2015: Watson verbal arithmetic

### October 2015: Counting 12 bits using 5-to-2 functions

### September 2015: Awarding N people with 8 multi-person teams

### August 2015: Loopsless projections of a loop

### July 2015: Four people with 1-6 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

### 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

### December 2013: Gifts graph

### November 2013: K-dim faces of d-dim 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

### 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

### 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

### 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

### 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: 5-ops 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

### 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 8-queen 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

### 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?

### 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*n-n)*f(n-1))/(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

### 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: 7-colored 35 beads necklace

### 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 read-only array

### December 2003: Similar dissection of quadrilaterals

### November 2003: Line intersecting curve in a pentagon

### October 2003: Non attacking new chess pieces

### 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

### 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

### 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

### 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: 2-dimensional 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

### December 1999: Zero-less 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

### 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