Chapter 9.3, Problem 42E

Solution

To identify: Are they all the same? Some recursively defined sequences are mathematical magic: Join up with three or four classmates and, without telling it to the others, pick a word from this sentence. Then, with care, count the letters in your word. Move ahead that many words in the text to come to a new word. Count the letters in the new word. Move ahead again, and so on. When you come to a point when your next move would take you out of this problem, stop. Share your last word with your friends.

Yes are they all the same

Given information:

The given word is ‘Join up with’

Explanation:

Need to randomly select a word in the exercise prompt from the second sentence. Next, count the number of letters in the word and move ahead that many words. Then repeat the procedure for the newly selected word until it would move us out of the exercise prompt.

For example, when select the word "Join", then the sequence of selected words would become: join, or, classmates, word, then, the, your, that, the, come, word, in, new, ahead, when, a, point, would, this, your, your, all. Thus the final selected word is then "all".

When select the word "up", then the sequence of selected words would become: up, three, without, word, then, the, your, that, the, come, word, in, new, ahead, when, a, point, would, this, your, your, all. Thus the final selected word is then "all".

When select the word "with", then the sequence of selected words would become: with, classmates, word, then, the, your, that, the, come, word, in, new, ahead, when, a, point, would, this, your, your, all. Thus the final selected word is then "all".

Note that always come out on the word "all", no matter which word we select from the sentence.

Yes are they all the same