Problem Solving

Hi,

I really didn't get this issue

please could you explain?

a vending machine dispenses gumballs in a regularly repeating cycle of 10 different colors
if a quarter buys 3 gumballs what is the minimum amount of money that must be spent before
3 gumballs of the same color are dispensed?

thks

$1.75.

21 would be the point at which your guaranteed to have 3 of the same color.

21/3=7

7*.25=1.75

backtoschool11 wrote:Let a, b, c be the three gumball colors we want repeated, and x be the other colors in the sequence that don't matter to us. Also let the number below the gumball sequence represent which quarter we are on.

a b c x x x x x x x a b c x x
1 1 1 2 2 2 3 3 3 4 4 4 5 5 5

As you can see, it will take a minimum of 5 quarters before we will have a repeat of our original three gumballs. IMO, the answer is $1.25.

What was the official answer?

"3 gumballs of the same color are dispensed" means 3 gum balls of the same color, not 3 gum balls that were the same as three gum balls we have seen before. This is reason it's important that the question mentioned they were 10 different colors. At least this is how I read the question. There may be some awkwardness of wording.

I would note that it asked for 3 gum balls of the same color, not the same colors. This would indicate that, for example, we're looking for the 3rd red gum ball, not a repeat of three different colored gum balls.

I understand the IMO-$2.50

sanyalpritish wrote:I understand the IMO-$2.50

Please explain your reasoning.

Ok create a Sque ABCDEFGHIJ-10 balls and next 10-Balls will be again ABCDEFGHIJ

in $.25 you get ABC next $.25 you get DEF next $.25 GHI and so on

Now the question is asking when will you get the same as Sque as anyone of these
ABC,DEF,GHI

If you do the above sque you will see that after 27 balls from the machine which is $(.25*9=$2.25) you will get one of these sque.

Not sure if this is clear or not

OA

francoisph wrote:Hi,

I really didn't get this issue

please could you explain?

a vending machine dispenses gumballs in a regularly repeating cycle of 10 different colors
if a quarter buys 3 gumballs what is the minimum amount of money that must be spent before
3 gumballs of the same color are dispensed?

thks

Hi Francoisph,

Answer should be $1.75
The question is asking for minimum amount to be spent to get 3 gumballs of the same colour.
Assuming that ABCDEFGHIJ to be the colours of the balls, we are looking for a combination where we can get AAA.
first quarter gives ABC, Second DEF, Third GHI, Fourth JAB, Fifth CDE, Sixth FGH, Seventh IJA
By this time we get 3 gumballs with A colour. So we need 7 quarters to get them.

So answer is 7*0.25 = 1.75$

Praveen

sk818020 wrote:

backtoschool11 wrote:Let a, b, c be the three gumball colors we want repeated, and x be the other colors in the sequence that don't matter to us. Also let the number below the gumball sequence represent which quarter we are on.

a b c x x x x x x x a b c x x
1 1 1 2 2 2 3 3 3 4 4 4 5 5 5

As you can see, it will take a minimum of 5 quarters before we will have a repeat of our original three gumballs. IMO, the answer is $1.25.

What was the official answer?

"3 gumballs of the same color are dispensed" means 3 gum balls of the same color, not 3 gum balls that were the same as three gum balls we have seen before. This is reason it's important that the question mentioned they were 10 different colors. At least this is how I read the question. There may be some awkwardness of wording.

I would note that it asked for 3 gum balls of the same color, not the same colors. This would indicate that, for example, we're looking for the 3rd red gum ball, not a repeat of three different colored gum balls.

Well, we are told that the machine dispenses the gumballs ina regularly repeating cycle of 10 different colors. So, the way you read the question is just fine, and I don't think there is a word awkwardness issue here.

But it seems that backtoschool fell into a different interpretation trap. If we interpret the question as: "what is the minimum that must be spent that will guarantee 3 gumballs each of the same color?", then the answer is $1.75. If we interpret the question as what is the minimum spent that COULD result in 3 gumballs of the same color, then the answer is $1.25. Based on the language of the question ("MUST be spent"..."3 gumballs of the same color ARE dispensed"), I would adopt the former interpretation.

So, the answer is $1.75.
___________

Hi guys,

Could someone explain clearly please?
step by step because I didnt get this issue !

thks

I understand now! I think the question wasn't clear in my mind!

ABC DEF GHI JAB CDE FGH IJA

We are looking for the combinaision, ABC, JAB, IJA; so we have 3*7 quarters(cyclce)= 21 balls
7*0.25$=1.75$

Thks All indeed

i think the answer will be $1.75

the question is three gum balls of the same color

and its given that the machine dispenses in a regular pattern

A b c d e f g h i j

A b c d e f g h i j

A b c d e f g h i j


let the first gumball be red (A)

then the next red gum ball would be the 11th(A) then the next would be the 21st(A)

so u need to get 21 gum balls to get three A's

and the 7th set of gum balls will get u the last red gumball

the first being (A b c) (d e f) (g h i) (j A b) (c d e) (f g h) (i j A)

one quarter gets u three gumballs, so u need seven quarters to get three same colored gumballs