Problem number 24. Amalia's machine changes one red token into three white tokens and one white token to two red tokens. Amalia has three red tokens and one white token. She uses the machine three times. What is the smallest number of tokens she can end up with? A, 7. B, 6. C, 8. D, 5. E, 9. We are trying to figure out what the smallest number of tokens that Amalia can get is. To do this, first notice that if we put a red token in the machine, we get three new tokens. But if we put a white token in the machine, we get two new tokens. So we need to put in white tokens as much as possible and avoid putting in red tokens if we want to find the smallest number. Here are the tokens Amalia started with. Since we're trying to put in white tokens whenever possible, let's put the white token in the machine. We will get two red tokens. This was our first use of the machine. For the second use, we will have to put in a red token and we get three white tokens. Now we can take one of those white tokens, put in the machine, and we get two red tokens. We have used the machine three times. Now we have 1, 2, 3, 4, 5, 6, 7, 8 tokens. The answer is C, 8.

token transformation

red tokens

white tokens

minimize tokens

optimal strategy