# Doc/Articles/AnswersToAPWJ

**At Play With J**

. *By* Eugene McDonnell.

# Answers to Problems for the Reader

In "At Play With J", Edition 1, there were 4 questions left as exercises for the reader. In Edition 2 we provide the answers in an Appendix.

The answers I've currently got are not necessarily the best. However I'm not going to hold up publication of the book for that reason. Instead the answers page in the book will carry a link to this Wiki page, which will serve to coordinate a leisurely discussion of answers.

If you wish to submit an answer, or criticise or improve an existing answer, please do so at the ends of the four papers concerned, viz.

Doc/Articles/Play113,

Doc/Articles/Play124,

Doc/Articles/Play164,

Doc/Articles/Play211,

not on this actual page. You will find answers already there.

From: Chapter 5: Jacobi's method

http://www.jsoftware.com/jwiki/Doc/Articles/Play113 [see midway down]

"Problem 1: Define a verb which takes as argument a positive even integer n and yields a permutation which, repeatedly applied to a conforming identity permutation, produces, in successive pairs of items, all possible choices of 2 items from n, with no duplications.

Problem 2: How many of the !n permutations of even order n are solutions to problem 1?"

From: Chapter 10: Years' Digits

http://www.jsoftware.com/jwiki/Doc/Articles/Play124 [see end-of-page]

"There is a solution to 91 which is shorter than this, by the way."

A fully-completed series of solutions needs to be provided, not just for number 91. IanClark

From: Chapter 23: An Open and Shut Case

http://www.jsoftware.com/jwiki/Doc/Articles/Play164 [see end-of-page]

"Here are the rest of the questions Amy had to answer. See if you can answer them.

A. What do you notice about the lockers that were touched by exactly two students? (Try >: m19 2=dc )

B. What do you notice about the lockers that were touched by exactly three students?

C. What do you notice about the lockers that were touched by exactly four students?

D. What was the first locker touched by both student 6 and student 8?

E. What do you notice about the student numbers of the students that touched both locker 24 and locker 36?

F. Which students touched both locker 100 and 120? What do you notice about their student numbers?"

From: Chapter 38: The Google Test

http://www.jsoftware.com/jwiki/Doc/Articles/Play211 [see end-of-page]

**Problem 2: Finding the sixth in a series**

You are given five 10-digit numbers from the digits of pi, and must find the sixth. Here are the numbers:

4338327950 2795028841 6939937510 3993751058 2110555964

Here they are, embedded in pi:

` 7 30 $ w`
`31415926535897932384626``4338327``95028841``971``693993751058``2097494`
`459230781640628620899862803482`
`534211706798214808651328230664`
`709384460955058223172535940812`
`84811174502841027019385``2110555``964``462294895493038196442881097`

The first and second overlap, as do the third and fourth.

I'll give two hints, the second vacuous:

*Hint 1:* Primarily, the sixth number has three doublets and overlaps the fifth.

*Hint 2:* Alternately, something for nothing.