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.
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Kaplan Teacher in Toronto
