These puzzles involve computing probabilities associated with dice. A die is a cube with faces marked with numbers 1 to 6, as in the figure here, and we assume that when a die is rolled, each number is equally likely to come out on top. The questions we ask are somewhat unusual, though. We have collected several facts that run counter to many people's intuitions. Our job is therefore both mathematical and psychologicalfirst, make the calculation, then, if the answer strains our intuition, try to reconcile the conflict through reasoning.
Readers are encouraged to submit prospective puzzles for future columns to email@example.com.
©2013 ACM 0001-0782/13/02
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and full citation on the first page. Copyright for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or fee. Request permission to publish from firstname.lastname@example.org or fax (212) 869-0481.
The Digital Library is published by the Association for Computing Machinery. Copyright © 2013 ACM, Inc.
"the number N of different numbers that appear is determined; for example, if the dice show 3,4,1,6,5,6, then N = 5, and if they show 6,2,2,3,6,2, then N = 3"
It's not clear how N is determined in the above example. What precisely is N supposed to represent?
With the dice showing 3,4,1,6,5,6, the numbers 1, 3, 4, 5, and 6 all appear, with 6 appearing more than once in this case. Because there are 5 different numbers represented, N=5. With 6, 2, 2, 3, 6, 2, only three numbers appear: 2, 3, and 6, so N=3.
Displaying all 2 comments