Petals Around the Rose

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The answer to this roll is six

Petals Around the Rose is a mathematical puzzle in which the object is to work out the formula by which a number is derived from the roll of a set of five dice. It is often used as an exercise in inductive reasoning.[1] The puzzle became popular in computer circles in the mid 1970s,[2] particularly through an anecdote recounted in Personal Computing which depicts Bill Gates working out the solution in an airport.[3]

Puzzle play[edit]

The puzzle is commonly presented as a game in which one person rolls the dice and announces a numerical result for each roll. Players are instructed to work out the pattern and announce the result of each roll themselves, but they are supposed to keep the formula for that result to themselves.[2][3]

The formula[edit]

The key to the formula is given by the name of the puzzle: the "rose" is the center dot which appears only on the 3 and 5 faces of a die, while the "petals" are the dots which surround the center dot. Therefore the numeric result can be calculated by counting 2 for each 3 face and 4 for each 5 face.[2] In the example above, there is one 5 and one 3 face, so the result is four plus two, or six.

See also[edit]


  1. ^ Reichert, Michael; Hawley, Richard (2010). Reaching Boys, Teaching Boys: Strategies that Work—and Why. John Wiley & Sons. pp. 54, 55. Retrieved 2012-12-04. 
  2. ^ a b c Morris, Scot (May 1980). "Games". Omni 2 (8): 144, 128. 
  3. ^ a b Borrett, Lloyd. "Bill Gates and Petals Around the Rose". Retrieved 2012-12-04.