id: 06617834
dt: j
an: 2016e.00923
au: Allen, Edward
ti: Random selection of 3-digit numbers.
so: Math. Spectr. 33, No. 1, 8-10 (2000).
py: 2000
pu: Applied Probability Trust (APT) c/o University of Sheffield, School of
Mathematics and Statistics (SoMaS), Sheffield
la: EN
cc: K90
ut: random experiments; random numbers; random variables; notation; probability
theory; estimated distribution; proofs
ci:
li:
ab: From the text: If 3-digit numbers are selected so that they differ from
each other in two or more positions, then the total possible number
selected is not unique but ranges from 50 to 100. This article examines
some problems in the random selection of 3-digit numbers; the study
originated in the following manner. In a regional mathematics contest,
students were to be examined so that their names remained anonymous.
Each student was assigned a unique random 3-digit identification number
to be written, in place of his or her name, on the answer sheet. To
reduce the possibility of a mix-up associated with any student putting
down the incorrect identification number, the numbers were randomly
selected so that each identification number differed from every other
one in at least two positions. A computer program was written that
randomly selected 3-digit numbers, each of which differed from the
others in at least two positions. The computations in the program
continued until no more numbers could be selected satisfying the
required condition. However, each time the program was run, a different
number of identification numbers was generated. This surprising result
motivated the present study. Of particular interest was the minimum
number, the average number, and the maximum number of identification
numbers that could be generated. After some notation is defined, an
analysis of the problem is presented. Additional research, suggested by
this study, is accessible to undergraduate students.
rv: