#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:
a = 1st digit 1
b = 2nd digit 7
c = 5th digit 0 
d = 6th digit 7
How many walks in Manhattan are there(not using broadways) from CORNER of min(a,b) and min(c,d) ave to max(a,b) st and max(c,d) ave
walking in positive direction 


A1. MY ANSWER TO THE FIRST ATTENDANCE QUESTION IS:
min(a, b) = 1, min(c,d) = 0
max(a,b) = 7, max(c,d) = 7
from (0, 1) to 7, 7
we can shrink the Manhattan by reducing height by 1. Then question becomes how many walk from (0, 0) to (7, 6)
F(7,6) = 1716




Q2. THE  SECOND ATTENDANCE QUESTION WAS:
Consider your RUID as a word of length 9 in the alpha bet
179007191 in the 10 "ALPHABET" (0-9). How many ways to rearrange your RUID. 


A2. MY ANSWER TO THE  SECOND ATTENDANCE QUESTION IS:

In my case, the full alphabet is 0,0,1,1,1,7,7,9,9
This question can be changed to manhattan walk of a 4-dimension lattice from (0,0,0,0) to (2, 3, 2, 2)
By using HW2's formular, we can calculate F(2,3,2,2) = (2+3+2+2)! / (2!*3!*2!*2!) = 7560