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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 July 2015 problem.
  • And now... here's our August 2015 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. August 2015: Loopsless projections of a loop

    Challenge Solution

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

    Challenge Solution

  3. June 2015: Drifting complex anomaly detection

    Challenge Solution

  4. May 2015: 3 people betting game

    Challenge Solution

  5. April 2015: 7x7x7 with as much Peters

    Challenge Solution

  6. March 2015: Punched (twice) tape

    Challenge Solution

  7. February 2015: Kakuro - hard version

    Challenge Solution

  8. January 2015: Kakuro - easy version

    Challenge Solution

  9. December 2014: A matrix with 29 solutions

    Challenge Solution

  10. November 2014: Distribution using two coins

    Challenge Solution

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

    Challenge Solution

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

    Challenge Solution

  13. August 2014: Biased binary search

    Challenge Solution

  14. July 2014: Pebbles game on a tetrahedron

    Challenge Solution

  15. June 2014: 25 intersecting Cubes

    Challenge Solution

  16. May 2014: Annihilation probability of 1D gun

    Challenge Solution

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

    Challenge Solution

  18. March 2014: Toggling lamps

    Challenge Solution

  19. February 2014: Juxtaposing a 4D pyramids

    Challenge Solution

  20. January 2014: Boolean 21x6 matrix

    Challenge Solution

  21. December 2013: Gifts graph

    Challenge Solution

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

    Challenge Solution

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

    Challenge Solution

  24. September 2013: Bob and Alice vs the casino

    Challenge Solution

  25. August 2013: Letters on a 9D hypercube

    Challenge Solution

  26. July 2013: Octahedronial dice

    Challenge Solution

  27. June 2013: Find a fraction

    Challenge Solution

  28. May 2013: Computing a polynomial

    Challenge Solution

  29. April 2013: Sum of fractions

    Challenge Solution

  30. March 2013: Buying 5 products

    Challenge Solution

  31. February 2013: Concatenating squares

    Challenge Solution

  32. January 2013: 13 permutation on 18 letters

    Challenge Solution

  33. December 2012: Maximal sum 6x6 grid

    Challenge Solution

  34. November 2012: Lattice of trees blocks light

    Challenge Solution

  35. October 2012: Disdyakis Triacontahedrons dice

    Challenge Solution

  36. September 2012: Parking game

    Challenge Solution

  37. August 2012: 3 charges that almost cancel out

    Challenge Solution

  38. July 2012: Coloring balls games

    Challenge Solution

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

    Challenge Solution

  40. May 2012: Permutation scheduling

    Challenge Solution

  41. April 2012: Garden hose model

    Challenge Solution

  42. March 2012: Balanced binary tree

    Challenge Solution

  43. February 2012: Biased coin game

    Challenge Solution

  44. January 2012: Exploding dragon egg

    Challenge Solution

  45. December 2011: Infinite chess game

    Challenge Solution

  46. November 2011: Volleyball tournament

    Challenge Solution

  47. October 2011: Interesting resistors network

    Challenge Solution

  48. September 2011: Bits to dice and back

    Challenge Solution

  49. August 2011: Triangle area / perimeter

    Challenge Solution

  50. July 2011: School lunches

    Challenge Solution

  51. June 2011: Parking density

    Challenge Solution

  52. May 2011: Distance between bad bars

    Challenge Solution

  53. April 2011: How many snakes

    Challenge Solution

  54. March 2011: Locating faulty bits

    Challenge Solution

  55. February 2011: Flippable number

    Challenge Solution

  56. January 2011: Letters and beans game

    Challenge Solution

  57. December 2010: Counting votes from percentage

    Challenge Solution

  58. November 2010: In honor of Benoit Mandelbrot

    Challenge Solution

  59. October 2010: Finding the size of a pentagon

    Challenge Solution

  60. September 2010: Threaded robot looks for a line

    Challenge Solution

  61. August 2010: Lilliput unique ID numbers

    Challenge Solution

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

    Challenge Solution

  63. June 2010: A bug in a Boolean circuit

    Challenge Solution

  64. May 2010: Quantization of probability vector

    Challenge Solution

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

    Challenge Solution

  66. March 2010: Spell names by passing phones

    Challenge Solution

  67. February 2010: 5 moves chess game

    Challenge Solution

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

    Challenge Solution

  69. December 2009: Finding 25 bits number using masks

    Challenge Solution

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

    Challenge Solution

  71. October 2009: Complete the sequence

    Challenge Solution

  72. September 2009: Non repeating cumulative sum

    Challenge Solution

  73. August 2009: Implement 3 nots using only 2

    Challenge Solution

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

    Challenge Solution

  75. June 2009: Value of expression regarding permutation

    Challenge Solution

  76. May 2009: Palindrome time

    Challenge Solution

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

    Challenge Solution

  78. March 2009: Hexadecimal exercise

    Challenge Solution

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

    Challenge Solution

  80. January 2009: Value of a replaceable lottery ticket

    Challenge Solution

  81. December 2008: Probability of random walk tetrominoes

    Challenge Solution

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

    Challenge Solution

  83. October 2008: Jumping frog

    Challenge Solution

  84. September 2008: Partitioning 13x13 to squares

    Challenge Solution

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

    Challenge Solution

  86. July 2008: Covering pentominoes by polyominos

    Challenge Solution

  87. June 2008: Probability of DNA testing

    Challenge Solution

  88. May 2008: Game of life - backwards

    Challenge Solution

  89. April 2008: Polygons formed from squares / triangles

    Challenge Solution

  90. March 2008: How much to bid?

    Challenge Solution

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

    Challenge Solution

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

    Challenge Solution

  93. December 2007: Finding intermittently failing parts

    Challenge Solution

  94. November 2007: Revealing sets of lights

    Challenge Solution

  95. October 2007: Resistance of Platonic solids

    Challenge Solution

  96. September 2007: Bundle deal of cable TV

    Challenge Solution

  97. August 2007: Describe the sequence

    Challenge Solution

  98. July 2007: Minimum length of blocking fence

    Challenge Solution

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

    Challenge Solution

  100. May 2007: Largest square in a cube

    Challenge Solution

  101. April 2007: Random walk of a frog

    Challenge Solution

  102. March 2007: Shooter / target game

    Challenge Solution

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

    Challenge Solution

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

    Challenge Solution

  105. December 2006: Cycles size in random permutation

    Challenge Solution

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

    Challenge Solution

  107. October 2006: Fraction of area of triangle

    Challenge Solution

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

    Challenge Solution

  109. August 2006: Value of future contract

    Challenge Solution

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

    Challenge Solution

  111. June 2006: Fraction of vertical dominoes

    Challenge Solution

  112. May 2006: Distance configuration of 4 points

    Challenge Solution

  113. April 2006: Random walk on a hypercube

    Challenge Solution

  114. March 2006: Expected area of random triangle

    Challenge Solution

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

    Challenge Solution

  116. January 2006: Size of smallest/largest piece

    Challenge Solution

  117. December 2005: Barring polyominoes from infinite board

    Challenge Solution

  118. November 2005: Size of finite random binary tree

    Challenge Solution

  119. October 2005: Matrices with special 2x2 minors

    Challenge Solution

  120. September 2005: Acceleration rate of pulley system

    Challenge Solution

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

    Challenge Solution

  122. July 2005: Covering table with coins

    Challenge Solution

  123. June 2005: Almost balanced A/B strings

    Challenge Solution

  124. May 2005: Rectangular grid / glass cubes

    Challenge Solution

  125. April 2005: Divisibility of integer powers

    Challenge Solution

  126. March 2005: 6x6x6 cube with different signatures

    Challenge Solution

  127. February 2005: Infinite right triangles

    Challenge Solution

  128. January 2005: 7-colored 35 beads necklace

    Challenge Solution

  129. December 2004: Projecting points onto the complex plane

    Challenge Solution

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

    Challenge Solution

  131. October 2004: GCD of values of primitive polynomial

    Challenge Solution

  132. September 2004: Another versions of turntable

    Challenge Solution

  133. August 2004: Longest way to come home

    Challenge Solution

  134. July 2004: N cups on a turntable

    Challenge Solution

  135. June 2004: Rectangles in the unit square

    Challenge Solution

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

    Challenge Solution

  137. April 2004: Labeling VCR cassettes using digit stickers

    Challenge Solution

  138. March 2004: Number of weakly monotone arrays

    Challenge Solution

  139. February 2004: Right isosceles triangle with integer sides

    Challenge Solution

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

    Challenge Solution

  141. November 2003: Line intersecting curve in a pentagon

    Challenge Solution

  142. December 2003: Similar dissection of quadrilaterals

    Challenge Solution

  143. October 2003: Non attacking new chess pieces

    Challenge Solution

  144. September 2003: Irrational root of polynomial

    Challenge Solution

  145. August 2003: Non attacking chess pieces

    Challenge Solution

  146. July 2003: Coloring roads to enable blind direction

    Challenge Solution

  147. June 2003: Partitioning a square into rectangles

    Challenge Solution

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

    Challenge Solution

  149. April 2003: Bounds on a Hamiltonian tour

    Challenge Solution

  150. March 2003: Fencing a pasture

    Challenge Solution

  151. February 2003: Zero sum in Boolean cards

    Challenge Solution

  152. January 2003: 4 points with odd integer distances

    Challenge Solution

  153. December 2002: 4 integers with squares sums

    Challenge Solution

  154. November 2002: 4 bottles on a square turntable

    Challenge Solution

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

    Challenge Solution

  156. September 2002: Closed subsets of boolean operators

    Challenge Solution

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

    Challenge Solution

  158. July 2002: 23 prisoners and a switch room

    Challenge Solution

  159. June 2002: Coin weighing using scale

    Challenge Solution

  160. May 2002: Circle passing via 7 lattice points

    Challenge Solution

  161. April 2002: Lifetime of adjacent differences

    Challenge Solution

  162. March 2002: Coffe or tea majority club

    Challenge Solution

  163. February 2002: Undirected graph of diameter 2

    Challenge Solution

  164. January 2002: Gambling casino

    Challenge Solution

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

    Challenge Solution

  166. November 2001: PB&J asymmetry bounds

    Challenge Solution

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

    Challenge Solution

  168. September 2001: Bounds on a permutation group

    Challenge Solution

  169. August 2001: Points on a plane

    Challenge Solution

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

    Challenge Solution

  171. June 2001: Goblin chase in a train

    Challenge Solution

  172. May 2001: Goblin chase in a pool

    Challenge Solution

  173. April 2001: College saving account

    Challenge Solution

  174. March 2001: Golf - hit in one

    Challenge Solution

  175. February 2001: Kubricia's 2001 money boxes

    Challenge Solution

  176. January 2001: Counting segments overlays

    Challenge Solution

  177. December 2000: Commuter gets 20 minutes earlier

    Challenge Solution

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

    Challenge Solution

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

    Challenge Solution

  180. September 2000: Simplify sqrt expression

    Challenge Solution

  181. August 2000: Six Card Cribbage

    Challenge Solution

  182. July 2000: 2-dimensional grid jumping coins

    Challenge Solution

  183. June 2000: Coins game (6.78$)

    Challenge Solution

  184. May 2000: Northwest to the north pole

    Challenge Solution

  185. April 2000: Revamp the tax code

    Challenge Solution

  186. March 2000: Sum of two squares

    Challenge Solution

  187. February 2000: N**C is integer

    Challenge Solution

  188. January 2000: Catching baseball

    Challenge Solution

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

    Challenge Solution

  190. November 1999: Cutting a cube into a box

    Challenge Solution

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

    Challenge Solution

  192. September 1999: Recognizing dishes

    Challenge Solution

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

    Challenge Solution

  194. July 1999: Labeling bowling pins

    Challenge Solution

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

    Challenge Solution

  196. May 1999: Integer side rectangles partition

    Challenge Solution

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

    Challenge Solution

  198. March 1999: Cliques of people in a ballroom

    Challenge Solution

  199. February 1999: A leashed sheep eats grass

    Challenge Solution

  200. January 1999: Water glass center of mass

    Challenge Solution

  201. December 1998: Removing snow

    Challenge Solution

  202. November 1998: Cutting frosted cake

    Challenge Solution

  203. October 1998: Sorting pancakes

    Challenge Solution

  204. September 1998: Magic Star of David

    Challenge Solution

  205. August 1998: Equilateral triangle

    Challenge Solution

  206. July 1998: Tennis balls in a bucket

    Challenge Solution

  207. June 1998: Shaking hands in a party

    Challenge Solution

  208. May 1998: A belt around the earth

    Challenge Solution