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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.

  • Here is the solution for our August 2016 problem.
  • And now... here's our September 2016 challenge!

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.

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

  1. September 2016: Seating four people for 24 hours

    Challenge Solution

  2. August 2016: Finding bags of counterfeit coins

    Challenge Solution

  3. July 2016: Pentominos tiling (Golomb)

    Challenge Solution

  4. June 2016: Tilting a truncated icosahedron

    Challenge Solution

  5. May 2016: Attacking chess pieces

    Challenge Solution

  6. April 2016: RoboCats falling by cubic polynomial

    Challenge Solution

  7. March 2016: Squareversed numbers

    Challenge Solution

  8. February 2016: IBM InterConnect

    Challenge Solution

  9. January 2016: Efficient bicycle gears

    Challenge Solution

  10. December 2015: EBCDIC to ASCII conversion

    Challenge Solution

  11. November 2015: Watson verbal arithmetic

    Challenge Solution

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

    Challenge Solution

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

    Challenge Solution

  14. August 2015: Loopsless projections of a loop

    Challenge Solution

  15. July 2015: Four people with 1-6 hats

    Challenge Solution

  16. June 2015: Drifting complex anomaly detection

    Challenge Solution

  17. May 2015: 3 people betting game

    Challenge Solution

  18. April 2015: 7x7x7 with as much Peters

    Challenge Solution

  19. March 2015: Punched (twice) tape

    Challenge Solution

  20. February 2015: Kakuro - hard version

    Challenge Solution

  21. January 2015: Kakuro - easy version

    Challenge Solution

  22. December 2014: A matrix with 29 solutions

    Challenge Solution

  23. November 2014: Distribution using two coins

    Challenge Solution

  24. October 2014: Last digits of 2^3^4^5^6^7^8^9

    Challenge Solution

  25. September 2014: 2^3^4^5 leading digit on base e

    Challenge Solution

  26. August 2014: Biased binary search

    Challenge Solution

  27. July 2014: Pebbles game on a tetrahedron

    Challenge Solution

  28. June 2014: 25 intersecting Cubes

    Challenge Solution

  29. May 2014: Annihilation probability of 1D gun

    Challenge Solution

  30. April 2014: 1D version of the 2048 game

    Challenge Solution

  31. March 2014: Toggling lamps

    Challenge Solution

  32. February 2014: Juxtaposing a 4D pyramids

    Challenge Solution

  33. January 2014: Boolean 21x6 matrix

    Challenge Solution

  34. December 2013: Gifts graph

    Challenge Solution

  35. November 2013: K-dim faces of d-dim hypercube

    Challenge Solution

  36. October 2013: B&W coloring of a chess board

    Challenge Solution

  37. September 2013: Bob and Alice vs the casino

    Challenge Solution

  38. August 2013: Letters on a 9D hypercube

    Challenge Solution

  39. July 2013: Octahedronial dice

    Challenge Solution

  40. June 2013: Find a fraction

    Challenge Solution

  41. May 2013: Computing a polynomial

    Challenge Solution

  42. April 2013: Sum of fractions

    Challenge Solution

  43. March 2013: Buying 5 products

    Challenge Solution

  44. February 2013: Concatenating squares

    Challenge Solution

  45. January 2013: 13 permutation on 18 letters

    Challenge Solution

  46. December 2012: Maximal sum 6x6 grid

    Challenge Solution

  47. November 2012: Lattice of trees blocks light

    Challenge Solution

  48. October 2012: Disdyakis Triacontahedrons dice

    Challenge Solution

  49. September 2012: Parking game

    Challenge Solution

  50. August 2012: 3 charges that almost cancel out

    Challenge Solution

  51. July 2012: Coloring balls games

    Challenge Solution

  52. June 2012: Dividing 1,506,009,006,001,500,000,000

    Challenge Solution

  53. May 2012: Permutation scheduling

    Challenge Solution

  54. April 2012: Garden hose model

    Challenge Solution

  55. March 2012: Balanced binary tree

    Challenge Solution

  56. February 2012: Biased coin game

    Challenge Solution

  57. January 2012: Exploding dragon egg

    Challenge Solution

  58. December 2011: Infinite chess game

    Challenge Solution

  59. November 2011: Volleyball tournament

    Challenge Solution

  60. October 2011: Interesting resistors network

    Challenge Solution

  61. September 2011: Bits to dice and back

    Challenge Solution

  62. August 2011: Triangle area / perimeter

    Challenge Solution

  63. July 2011: School lunches

    Challenge Solution

  64. June 2011: Parking density

    Challenge Solution

  65. May 2011: Distance between bad bars

    Challenge Solution

  66. April 2011: How many snakes

    Challenge Solution

  67. March 2011: Locating faulty bits

    Challenge Solution

  68. February 2011: Flippable number

    Challenge Solution

  69. January 2011: Letters and beans game

    Challenge Solution

  70. December 2010: Counting votes from percentage

    Challenge Solution

  71. November 2010: In honor of Benoit Mandelbrot

    Challenge Solution

  72. October 2010: Finding the size of a pentagon

    Challenge Solution

  73. September 2010: Threaded robot looks for a line

    Challenge Solution

  74. August 2010: Lilliput unique ID numbers

    Challenge Solution

  75. July 2010: 1,000,000,000 divides round((1+2cos(20))**n)

    Challenge Solution

  76. June 2010: A bug in a Boolean circuit

    Challenge Solution

  77. May 2010: Quantization of probability vector

    Challenge Solution

  78. April 2010: Hex = dec, removing last 21 digits

    Challenge Solution

  79. March 2010: Spell names by passing phones

    Challenge Solution

  80. February 2010: 5 moves chess game

    Challenge Solution

  81. January 2010: Make a 5 from 2 and 2

    Challenge Solution

  82. December 2009: Finding 25 bits number using masks

    Challenge Solution

  83. November 2009: Fastest way to find the smallest divisor

    Challenge Solution

  84. October 2009: Complete the sequence

    Challenge Solution

  85. September 2009: Non repeating cumulative sum

    Challenge Solution

  86. August 2009: Implement 3 nots using only 2

    Challenge Solution

  87. July 2009: Ending a backgammon game with a double

    Challenge Solution

  88. June 2009: Value of expression regarding permutation

    Challenge Solution

  89. May 2009: Palindrome time

    Challenge Solution

  90. April 2009: 5-ops implementation of erasure code

    Challenge Solution

  91. March 2009: Hexadecimal exercise

    Challenge Solution

  92. February 2009: Find a bug in this unknown riddle

    Challenge Solution

  93. January 2009: Value of a replaceable lottery ticket

    Challenge Solution

  94. December 2008: Probability of random walk tetrominoes

    Challenge Solution

  95. November 2008: Ponder^this = ponder...

    Challenge Solution

  96. October 2008: Jumping frog

    Challenge Solution

  97. September 2008: Partitioning 13x13 to squares

    Challenge Solution

  98. August 2008: Variation on the 8-queen problem

    Challenge Solution

  99. July 2008: Covering pentominoes by polyominos

    Challenge Solution

  100. June 2008: Probability of DNA testing

    Challenge Solution

  101. May 2008: Game of life - backwards

    Challenge Solution

  102. April 2008: Polygons formed from squares / triangles

    Challenge Solution

  103. March 2008: How much to bid?

    Challenge Solution

  104. February 2008: What are the rules of the game?

    Challenge Solution

  105. January 2008: Buying random balls out of an urn

    Challenge Solution

  106. December 2007: Finding intermittently failing parts

    Challenge Solution

  107. November 2007: Revealing sets of lights

    Challenge Solution

  108. October 2007: Resistance of Platonic solids

    Challenge Solution

  109. September 2007: Bundle deal of cable TV

    Challenge Solution

  110. August 2007: Describe the sequence

    Challenge Solution

  111. July 2007: Minimum length of blocking fence

    Challenge Solution

  112. June 2007: Sum of random (0,1) game

    Challenge Solution

  113. May 2007: Largest square in a cube

    Challenge Solution

  114. April 2007: Random walk of a frog

    Challenge Solution

  115. March 2007: Shooter / target game

    Challenge Solution

  116. February 2007: When to discard a random number?

    Challenge Solution

  117. January 2007: Future contracts - how many to buy?

    Challenge Solution

  118. December 2006: Cycles size in random permutation

    Challenge Solution

  119. November 2006: Expressions with 1,2,3,4

    Challenge Solution

  120. October 2006: Fraction of area of triangle

    Challenge Solution

  121. September 2006: f(n)=(1+(n*n-n)*f(n-1))/(n*n+1)

    Challenge Solution

  122. August 2006: Value of future contract

    Challenge Solution

  123. July 2006: Approximations of 1/x and sqrt(x)

    Challenge Solution

  124. June 2006: Fraction of vertical dominoes

    Challenge Solution

  125. May 2006: Distance configuration of 4 points

    Challenge Solution

  126. April 2006: Random walk on a hypercube

    Challenge Solution

  127. March 2006: Expected area of random triangle

    Challenge Solution

  128. February 2006: Random [0,1] poker game

    Challenge Solution

  129. January 2006: Size of smallest/largest piece

    Challenge Solution

  130. December 2005: Barring polyominoes from infinite board

    Challenge Solution

  131. November 2005: Size of finite random binary tree

    Challenge Solution

  132. October 2005: Matrices with special 2x2 minors

    Challenge Solution

  133. September 2005: Acceleration rate of pulley system

    Challenge Solution

  134. August 2005: first N digits of M is divisible by N

    Challenge Solution

  135. July 2005: Covering table with coins

    Challenge Solution

  136. June 2005: Almost balanced A/B strings

    Challenge Solution

  137. May 2005: Rectangular grid / glass cubes

    Challenge Solution

  138. April 2005: Divisibility of integer powers

    Challenge Solution

  139. March 2005: 6x6x6 cube with different signatures

    Challenge Solution

  140. February 2005: Infinite right triangles

    Challenge Solution

  141. January 2005: 7-colored 35 beads necklace

    Challenge Solution

  142. December 2004: Projecting points onto the complex plane

    Challenge Solution

  143. November 2004: Sum of numbers after worm ate some

    Challenge Solution

  144. October 2004: GCD of values of primitive polynomial

    Challenge Solution

  145. September 2004: Another versions of turntable

    Challenge Solution

  146. August 2004: Longest way to come home

    Challenge Solution

  147. July 2004: N cups on a turntable

    Challenge Solution

  148. June 2004: Rectangles in the unit square

    Challenge Solution

  149. May 2004: A twist on "Towers of Hanoi" puzzle

    Challenge Solution

  150. April 2004: Labeling VCR cassettes using digit stickers

    Challenge Solution

  151. March 2004: Number of weakly monotone arrays

    Challenge Solution

  152. February 2004: Right isosceles triangle with integer sides

    Challenge Solution

  153. January 2004: Finding duplicates in read-only array

    Challenge Solution

  154. December 2003: Similar dissection of quadrilaterals

    Challenge Solution

  155. November 2003: Line intersecting curve in a pentagon

    Challenge Solution

  156. October 2003: Non attacking new chess pieces

    Challenge Solution

  157. September 2003: Irrational root of polynomial

    Challenge Solution

  158. August 2003: Non attacking chess pieces

    Challenge Solution

  159. July 2003: Coloring roads to enable blind direction

    Challenge Solution

  160. June 2003: Partitioning a square into rectangles

    Challenge Solution

  161. May 2003: sqrt(1+2*sqrt(1+3*sqrt(...+n*sqrt(1]

    Challenge Solution

  162. April 2003: Bounds on a Hamiltonian tour

    Challenge Solution

  163. March 2003: Fencing a pasture

    Challenge Solution

  164. February 2003: Zero sum in Boolean cards

    Challenge Solution

  165. January 2003: 4 points with odd integer distances

    Challenge Solution

  166. December 2002: 4 integers with squares sums

    Challenge Solution

  167. November 2002: 4 bottles on a square turntable

    Challenge Solution

  168. October 2002: Tournament of N with <=M players

    Challenge Solution

  169. September 2002: Closed subsets of boolean operators

    Challenge Solution

  170. August 2002: Drawing 4D hypercube on a grid

    Challenge Solution

  171. July 2002: 23 prisoners and a switch room

    Challenge Solution

  172. June 2002: Coin weighing using scale

    Challenge Solution

  173. May 2002: Circle passing via 7 lattice points

    Challenge Solution

  174. April 2002: Lifetime of adjacent differences

    Challenge Solution

  175. March 2002: Coffe or tea majority club

    Challenge Solution

  176. February 2002: Undirected graph of diameter 2

    Challenge Solution

  177. January 2002: Gambling casino

    Challenge Solution

  178. December 2001: Knight's tour on 4xN chess boards

    Challenge Solution

  179. November 2001: PB&J asymmetry bounds

    Challenge Solution

  180. October 2001: f maps any open interval onto R

    Challenge Solution

  181. September 2001: Bounds on a permutation group

    Challenge Solution

  182. August 2001: Points on a plane

    Challenge Solution

  183. July 2001: 1/1 + 2/(2+3) + 3/(4+5+6) + ...

    Challenge Solution

  184. June 2001: Goblin chase in a train

    Challenge Solution

  185. May 2001: Goblin chase in a pool

    Challenge Solution

  186. April 2001: College saving account

    Challenge Solution

  187. March 2001: Golf - hit in one

    Challenge Solution

  188. February 2001: Kubricia's 2001 money boxes

    Challenge Solution

  189. January 2001: Counting segments overlays

    Challenge Solution

  190. December 2000: Commuter gets 20 minutes earlier

    Challenge Solution

  191. November 2000: 75 integers in [1,230]

    Challenge Solution

  192. October 2000: One+five(four) cards trick

    Challenge Solution

  193. September 2000: Simplify sqrt expression

    Challenge Solution

  194. August 2000: Six Card Cribbage

    Challenge Solution

  195. July 2000: 2-dimensional grid jumping coins

    Challenge Solution

  196. June 2000: Coins game (6.78$)

    Challenge Solution

  197. May 2000: Northwest to the north pole

    Challenge Solution

  198. April 2000: Revamp the tax code

    Challenge Solution

  199. March 2000: Sum of two squares

    Challenge Solution

  200. February 2000: N**C is integer

    Challenge Solution

  201. January 2000: Catching baseball

    Challenge Solution

  202. December 1999: Zero-less multiply of 2**1999

    Challenge Solution

  203. November 1999: Cutting a cube into a box

    Challenge Solution

  204. October 1999: Path 1 or 2 in directed graph

    Challenge Solution

  205. September 1999: Recognizing dishes

    Challenge Solution

  206. August 1999: Seating people on N+M tables

    Challenge Solution

  207. July 1999: Labeling bowling pins

    Challenge Solution

  208. June 1999: 1 plus 1/7 of the medals

    Challenge Solution

  209. May 1999: Integer side rectangles partition

    Challenge Solution

  210. April 1999: Wally's Rock Permuting (WRP)

    Challenge Solution

  211. March 1999: Cliques of people in a ballroom

    Challenge Solution

  212. February 1999: A leashed sheep eats grass

    Challenge Solution

  213. January 1999: Water glass center of mass

    Challenge Solution

  214. December 1998: Removing snow

    Challenge Solution

  215. November 1998: Cutting frosted cake

    Challenge Solution

  216. October 1998: Sorting pancakes

    Challenge Solution

  217. September 1998: Magic Star of David

    Challenge Solution

  218. August 1998: Equilateral triangle

    Challenge Solution

  219. July 1998: Tennis balls in a bucket

    Challenge Solution

  220. June 1998: Shaking hands in a party

    Challenge Solution

  221. May 1998: A belt around the earth

    Challenge Solution