# Gumball Problem

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• Published : January 3, 2011

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1.Three cents is the most Ms. Hernandez might have to spend to get both her twins the same colored gumballs if there are only white and red gumballs. This is because for the first penny she uses there is a 50% Ms. Hernandez can get a red gumball and a 50% chance she can get a red one. For the second and third she has the same chances. The chart below shows all the possible combinations of gumballs Ms. Hernandez could have gotten. PenniesColor

1st PennyRed
2nd PennyWhite
3rd Penny Red
1st PennyWhite
2nd PennyRed
3rd PennyWhite

2.The next day Ms. Hernandez and her twins pass another gumball machine with three colors, red, white, and blue and again her twins want the same color. The most Ms. Hernandez might have to spend is 4 cents. This is because she could get the following: PenniesColor

1stRed
2ndWhite
3rdBlue
4thWhite

3.Seven cents is the most Mr. Hodges might have to spend to get his triplets the same color gumballs at the same three-color gumball machine as Ms. Hernandez. This is because he could get the following:

PenniesColors
1st pennyBlue
2nd pennyRed
3rd pennyWhite
4th pennyWhite
5th pennyBlue
6th penny Red
7th pennyBlue

4.The next day Mr. Hodges passes a two-color (red and white) gumball machine with his triplets again, they each want the same color. The most Mr. Hodges would have to spend is 5 cents. This is because he can get the following:

PenniesColor
1st pennyRed
2nd pennyWhite
3rd pennyWhite
4th pennyRed
5th pennywhite

5.The formula I found to solve these problems is: [(# of colors)(of kids)]- [(#of colors)-1]= how much money they need to spend. Ex of formula for question #1 is: [(2 colors)(2 kids)]-[(2 colors)-1]= 3 cents Ex of formula for question #2 is: [(3 colors)(2 kids)]- [(3 colors)-1]= 4 cents Ex of formula for question #3 is: [(3 colors)(3kids)]-[(3 colors)-1]= 7 cents Ex of formula for question #4 is: [(2 colors)(3...