Gumball Problem

Three cents is the most Ms. Hernandez authority accept to exhaust to get twain her twins the selfselfcorresponding tingeed gumballs if there are merely clear and red gumballs. This is accordingly for the foremost gentleman she uses there is a 50% Ms. Hernandez can get a red gumball and a 50% random she can get a red one. For the prevent and third she has the selfselfcorresponding randoms. The chart underneath shows all the potential combinations of gumballs Ms. Hernandez could accept gotten. PenniesColor 1st PennyRed 2nd PennyWhite 3rd Gentleman Red st PennyWhite 2nd PennyRed 3rd PennyWhite 2. The direct day Ms. Hernandez and her twins by another gumball agent delay three tinges, red, clear, and bluish and anew her twins nonproduction the selfselfcorresponding tinge. The most Ms. Hernandez authority accept to exhaust is 4 cents. This is accordingly she could get the following: PenniesColor 1stRed 2ndWhite 3rdBlue 4thWhite 3. Seven cents is the most Mr. Hodges authority accept to exhaust to get his triplets the selfselfcorresponding tinge gumballs at the selfselfcorresponding three-tinge gumball agent as Ms. Hernandez. This is accordingly he could get the following: PenniesColors 1st gentlemanBlue 2nd gentlemanRed 3rd gentlemanWhite 4th gentlemanWhite 5th gentlemanBlue 6th gentleman Red 7th gentlemanBlue 4. The direct day Mr. Hodges byes a two-tinge (red and clear) gumball agent delay his triplets anew, they each nonproduction the selfselfcorresponding tinge. The most Mr. Hodges would accept to exhaust is 5 cents. This is accordingly he can get the following: PenniesColor 1st gentlemanRed 2nd gentlemanWhite 3rd gentlemanWhite 4th gentlemanRed 5th gentlemanclear . The formula I plant to reresolve these completions is: [(# of tinges)(of kids)]- [(#of tinges)-1]= how greatly coin they demand to exhaust. Ex of formula for topic #1 is: [(2 tinges)(2 kids)]-[(2 tinges)-1]= 3 cents Ex of formula for topic #2 is: [(3 tinges)(2 kids)]- [(3 tinges)-1]= 4 cents Ex of formula for topic #3 is: [(3 tinges)(3kids)]-[(3 tinges)-1]= 7 cents Ex of formula for topic #4 is: [(2 tinges)(3 kids)]-[(2 tinges)-1]= 5 centsI figured this formula out by writing out how kids and tinges in each completion and then the utmost whole spent behind I plant each response. Ex: Completion 1: 2 kids, 2 tinges, max spent: 4. I knew that two this demanded to be multiplied and this demanded to be subtracted so I did a conjecture and repress until I plant the response.