> #ATTENDANCE QUIZ FOR LECTURE 2 of Dr. Z.'s Math454(02) Rutgers University
> 
> # Please Edit this .txt page with Answers
> 
> #Email  ShaloshBEkhad@gmail.com 
> #Subject: p2
> #with an attachment called
> #p2FirstLast.txt
> #(e.g. p2DoronZeilberger.txt)
> 
> #Right after finishing watching the Second lecture but no later than Friday, Sept. 11, 2020, 8:00pm
> 
> 
> 
> 
> #Q1. THE FIRST ATTENDANCE QUESTION WAS:
> #ATTENDANCE QUESTION #1
;
> #Let a: = FIRST DIGIT of your RUID
;
> 
;
> #Let b: = SECOND DIGIT of your RUID
;
> #Let b: = FIFTH DIGIT of your RUID
;
> #Let d: = SIXTH DIGIT of your RUID
;
> #HOW MANY WALKS IN MANHATTAN ARE THERE (NOT USING BDWAY)
;
> #From CORNER of min(a, b) St and  min(c, d) Ave
;
> #to   CORNER OF max(a, b  St and  max(c, d) Ave
;
> #Walking in the positive direction
;
> #A1. MY ANSWER TO THE FIRST ATTENDANCE QUESTION IS:

> F:=proc(m,n) option remember:
> 
> if m<0 or n<0 then
> 
> 0:
> 
> elif m=0 and n=0 then
> 
> 1:
> 
> else
> 
> F(m-1,n)+F(m,n-1):
> 
> fi:
> 
> end:
> 
;
> a := 1
a := 1
;
> b := 7
b := 7
;
> c := 0
c := 0
;
> d := 7
d := 7
;
> #corner1
;
> min(a, b)
1
;
> min(c, d)
0
;
> #corner
;
> max(a, b)
7
;
> max(c, d)
7
;
> #From(1,0) to (7,7) = From(0,0) to (6, 7)
;
> F(6,7)
1716
;
> #There are 1716 Walks
;
> #Q2. THE  SECOND ATTENDANCE QUESTION WAS:
> 
> 
;
> #SECOND ATTENDANCE QUESTION FOR LECTURE 2
;
> #CONSIDER YOUR RUID AS A WORD of LENGTH 9 in
;
> #THE 10-LETTER "ALPHABET" {0,1,2,3,4,5,6,7,8,9}
;
> #HOW MANY WAYS TO REARRANGE YOUR RUID?
;
> 
> #A2. MY ANSWER TO THE  SECOND ATTENDANCE QUESTION IS:
> NuW:=proc(L) local k,i:
> option remember:
> 
> k:=nops(L):
> 
> if min(op(L))<0 then
>  0:
> elif L=[0$k] then
>  1:
> else
> add(NuW([op(1..i-1,L),L[i]-1,op(i+1..k,L)]),i=1..k):
> fi:
> 
> end:
> ID := [1,7,9,0,0,7,5,2,1]
ID := [1, 7, 9, 0, 0, 7, 5, 2, 1]
;
> sort(ID)
[0, 0, 1, 1, 2, 5, 7, 7, 9]
;
> F := [2,2,1,1,2,1]
F := [2, 2, 1, 1, 2, 1]
;
> NuW(F)
45360
;
> #Answer: there are 45360 ways to rearrange my RUID
;