Archived Stumpers (with solutions)
STUMPER #1.15: MEDICAL MATH
(Did you solve something differently? There's almost always more than one way to solve
a math problem. Sometimes there's even more than one correct solution!)
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1. Math Pills
___You’re suffering from Acute Math Deficiency! You rush to the doctor, who gives you three pills and tells you to take one every half hour. How long will it be before you run out of pills?
1 hour. (You take the first one right now, and the last one an hour from now).
2. Germ Jar
___A germ is in a jar. After one minute, it splits and becomes 2. In another minute, each of those split again, so there are 4. In the next minute, each splits again, making 8. The entire jar is full in 1 hour. How long would it take to fill the jar if you started with 2 germs instead of one?
59 minutes. In the original problem, there were 2 germs after the first minute, and it took 59 more minutes after that to fill the jar.
3. Measuring Medicine
__ A mother has three sick children. Each needs 8 ounces of medicine. She has a 24-ounce bottle of medicine and three other containers, which measure 5, 11, and 13 ounces. She has no way to wash the containers and her children refuse to drink out of the same containers. How can she divide the medicine so each child gets exactly 8 ounces without having any of them drink from the same container?
Fill the 5 oz. and 11 oz. containers from the 24 oz. container. This leaves 8 oz in the 24 oz. bottle, so one child can drink that. Next, empty the 11 oz. bottle by pouring the contents into the 13 oz. bottle. Fill the 13 oz. bottle from the 5 oz. container (with 2 oz.) and put the 3 remaining oz from the 5 oz. container in the 11-ounce bottle. Fill the 5 oz bottle from the 13-oz one, and then pour all 5 oz into the 11 oz bottle. There are now 8 ounces in the 11-oz bottle and 8 in the 13-oz container.