SOLUTION: Use a generating function to model the problem: How many ways are there to make change for $0.62 using only pennies, nickels, and dimes so that the total number of coins used is ev

Question 1078159: Use a generating function to model the problem: How many ways are there to make change for $0.62 using only pennies, nickels, and dimes so that the total number of coins used is even?
Answer by ikleyn(52903) (Show Source): You can put this solution on YOUR website!
.

1.  On the method of generating function/functions to solve coin problems see the pretty fine explanation at the link

    http://www.cs.cmu.edu/afs/cs.cmu.edu/academic/class/15251-f10/Site/Materials/Lectures/Lecture09/lecture09.pdf

    http://www.cs.cmu.edu/afs/cs.cmu.edu/academic/class/15251-f10/Site/Materials/Lectures/Lecture09/lecture09.pdf



2.  But I think that the GIVEN particular problem can be solved faster and easier DIRECTLY and EXPLICITLY:


   2 pennies  +  0 dimes   + 12 nickels
   2 pennies  +  2 dimes   +  8 nickels
   2 pennies  +  4 dimes   +  4 nickels
   2 pennies  +  6 dimes   +  0 nickels

   7 pennies  +  0 dimes   + 11 nickels
   7 pennies  +  2 dimes   +  7 nickels
   7 pennies  +  4 dimes   +  3 nickels

  12 pennies  +  0 dimes   + 10 nickels
  12 pennies  +  2 dimes   +  6 nickels
  12 pennies  +  4 dimes   +  2 nickels

  17 pennies  +  0 dimes   +  9 nickels
  17 pennies  +  2 dimes   +  5 nickels
  17 pennies  +  4 dimes   +  1 nickels

  22 pennies  +  0 dimes   +  8 nickels
  22 pennies  +  2 dimes   +  4 nickels
  22 pennies  +  4 dimes   +  0 nickels

  27 pennies  +  0 dimes   +  7 nickels
  27 pennies  +  2 dimes   +  3 nickels

  32 pennies  +  0 dimes   +  6 nickels
  32 pennies  +  2 dimes   +  2 nickels

  37 pennies  +  0 dimes   +  5 nickels
  37 pennies  +  2 dimes   +  1 nickels

  42 pennies  +  0 dimes   +  4 nickels
  42 pennies  +  2 dimes   +  0 nickels

  47 pennies  +  0 dimes   +  3 nickels

  52 pennies  +  0 dimes   +  2 nickels

  57 pennies  +  0 dimes   +  1 nickels

  62 pennies  +  0 dimes   +  0 nickels


In this way I counted 28 possibilities.


So, my answer is:  28 possibilities.

RELATED QUESTIONS
Make a systematic list to solve the following problem: how many ways are there to make... (answered by richwmiller)

How many different ways are there to make 52 cents using only dimes and... (answered by Alan3354)

How many ways using pennies dimes nickles and quarters are there to make 55 cents (answered by ikleyn)

How many coin combinations are there to make $4.30 only using quarters, nickles, dimes,... (answered by Edwin McCravy)

Please help me solve this word problem. How can you make change for a dollar using... (answered by Edwin McCravy,mathanator)

In how many different ways can you make change for one dollar without using... (answered by Edwin McCravy)

HOW MANY DIFFERENT WAYS CAN YOU MAKE CHANGE FOR A 50-CENT COIN BY USING QUARTERS,... (answered by MathLover1)

Would like to see the solution for the following problem: How many ways can you make... (answered by Edwin McCravy)

using only quaters dimes and nickles how many different ways are there to make a total of (answered by Edwin McCravy)