Expert: Paul Klarreich - 6/15/2008

Question
1. There are 10 empty places in a crossword type puzzle. each empty place has 2 or 3 choices. (6 empty places has 2 choices and 4 empty places has 3 choices) only one choice is correct.

What is the maximum number of solution for this crossword puzzle? Pls answer in detail and in easy way. Thx
(all choices are independent)

2. Is there any software who can make the list of all these choices? if yes, which one
(if it can be done on spss, pls tell me how)


Answer
Questioner:   Munir
Category:  Advanced Math
Private:  No
 
Subject:  crossword type puzzle
Question:  1. There are 10 empty places in a crossword type puzzle. each empty place has 2 or 3 choices. (6 empty places has 2 choices and 4 empty places has 3 choices) only one choice is correct.

What is the maximum number of solution for this crossword puzzle? Pls answer in detail and in easy way. Thx
(all choices are independent)

2. Is there any software who can make the list of all these choices? if yes, which one
(if it can be done on spss, pls tell me how)
.....................................................

Hi, Munir,

This is just the Basic Counting Principle: If one thing can be done N ways, and another in M ways, then the number of ways they can both be done is N*M.

In this case it's just:

2 2 2 2 2 2 3 3 3 3 = 2^6 3^4

What's an spss?