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Prob Solving in Discrete Math

by: Mrs. Dangelo Fahey

Prob Solving in Discrete Math MATH 6105

Mrs. Dangelo Fahey
GPA 3.73


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This 3 page Class Notes was uploaded by Mrs. Dangelo Fahey on Sunday October 25, 2015. The Class Notes belongs to MATH 6105 at University of North Carolina - Charlotte taught by Staff in Fall. Since its upload, it has received 47 views. For similar materials see /class/228921/math-6105-university-of-north-carolina-charlotte in Mathematics (M) at University of North Carolina - Charlotte.


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Date Created: 10/25/15
SWIM 2007 1 For each of the following problems7 let Sn F 9 Math 6105 n in case n is a single digit integer If n 2 10 is an integer7 Sn is the sum of the digits of 71 Similarly Pn is n if n is a positive single digit integer and the product of the digits of n otherwise If there is not solution7 prove it a What is the smallest solution to Sn 2005 Express your answer in exponential notation Find all solutions to SSSn SSn Sn 100 Find all solutions to SSn Sn n 2007 2007 North Carolina High School Math Contest Find the sum 51 52 82007 Recall the two functions oor and fractional part de ned by is the largest integer that is less than or equal to 7 and z 7 a For each member z of the set S S 7T12347 7123473797 evaluate ltzgt and b De ne another function f by f x 7 10ll7moj Find f and for each x in S c Let g 7 10lj Evaluate g at each of the members of S d Prove that for any number x 100a 10b c f7 where a is a positive integer7 b is a digit7 c is a digit7 and 0 S f lt 17 g b In other words7 g is the tens digit of x Let 17 b7 0 d7 and e be digits satisfying 4 abode4 4abcde Find all ve of the digits a Grab a calculator You might not be able to do this one in your head b Key in the rst three digits of your phone number NOT the area code c Multiply by 80 d Add 1 e Multiply by 250 f Add the last 4 digits of your phone number g Add the last 4 digits of your phone number AGAIN h Subtract 250 SWIM 2007 Math 6105 U 03 I 00 p i Divide number by 2 Explain why you get such an interesting answer This problem is part of an email message I received from a friend 77This is pretty neat Can you gure out the trick I usually just accept these kinds of things and enjoy them rather than trying to second guess them OUT TO DINNER MATHEMATICS This is pretty neat how it works out DON7T CHEAT BY SCROLLING DOWN FIRST It takes less than a minute Work this out as you read Don7t cheat and read the bottom until you7ve worked through it This is fun First of all7 pick the number of times a week that you would like to have dinner out try for more than once but less than 10 Multiply this number by 2 Just to be bold Add 5 Just because Multiply it by 50 I7ll wait while you get the calculator If you have already had your birthday this year add 1755 If you haven7t7 add 1754 Now subtract the four digit year that you were born You should have a three digit number The rst digit of this was your original number How many times you want to eat out each week The next two num bers are YOUR AGE Oh YES7 it ISIIIII THIS IS THE ONLY YEAR 2005 IT WILL EVER WORK7 SO SPREAD IT AROUND WHILE IT LASTS IMPRESSIVE7 ISN7T IT77 The problem is to explain why this works A two digit integer N that is not a multiple of 10 is k times the sum of its digits The number formed by interchanging the digits is m times the sum of the digits What is the relationship between m and k The do challenge httpdigicccom do The crystal cabobble challenge httpwwwsinotradinguscrystalballhtm How many two digit positive integers N have the property that the sum of N and the number obtained by reversing the order of the digits of N is a perfect square A check is written for z dollars and y cents7 both z and y two digit numbers In error it is cashed for y dollars and z cents7 the incorrect amount exceeding the correct amount by 1782 Find a possible value for z and y 2 SWIM 2007 Math 6105 11 H D H 9 Solve the alpha numeric problem 2abc gtlt 4 cbaQ7 where 17 b and c are decimal digits ln problems 12 and 137 we are dealing with six digit numbers The rightmost digit of a six digit number N is moved to the left end The new number obtained is ve times N What is N Repeat the same problem with the 5 Changed to a 4 That is 4abcdef fabcde Let N 1234567891011 19992000 be the integer obtained by appending the decimal representations of the numbers from 1 to 2000 together in order What is the remainder when N is divided by 9


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