Brain Teasers
Hungry Termites
You have two very hungry termites and two sticks of wood. One stick of wood is 12 inches long and the other is 16 inches long. One termite can eat sticks at the rate of 1 inch every 3 minutes. The other termite can eat 1 inch in 4 minutes. How would you use the termites and sticks to measure 61 minutes?
Answer
Start the slow termite eating the longer stick. It will take the slow termite 16 minutes to eat the 4 inches that will make the sticks the same size. When the sticks are the same size, start the fast termite on the other stick. This termite will finish his 12 inch stick in 36 minutes. That's 52 minutes elapsed so far and the slow termite still has 3 inches left on his stick. Remove the slow termite and let the fast termite finish off the 3 inches in 9 minutes for a total of 61 minutes.Hide Answer Show Answer
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Comments
Good teaser. But how would you use the termites to devore the sticks in the sortest time?
Good job. Hehe, I reviewed this one
Jmcleod, I thought of an answer for the termites to eat the total of the sticks in 36 minutes. Start the fast termite on the 12 inch stick and the slow termite on the 16 inch stick. It will take the fast termite 36 minutes to finish the 12 inch stick and meanwhile the slow termite will have eaten 9 inches of the 16 inch stick. As soon as the fast termite finishes the 12 inch stick, start it on the other end of the 16 inch stick. This will take them 12 minutes to finish the entire of the stick, making a total of 36 minutes.
horse luver, I used the same logic you used, but came up with 48 min. 36 to finish the 12 stick and 9 inches of the longer stick, and 12 min working together to finish the last 7 inches of the longer stick. I don't think there is a faster way.
The termite is NOT slow! He is special! Loved this teaser, even though I hate math!
jmcleod: You're right. It can't be done any faster than 48 minutes. Here's why: the sum of the eating rates of the termites is 3 inches in 12 minutes plus 4 inches in 12 minutes, or 7 inches in 12 minutes. Thus, 28 inches (12 plus 16), which is 4 times 7 inches, can be eaten in no less than 4 times 12 minutes, or 48 minutes.
hey guyz just give the 3min termite eater 7 sticks and the 4min termite eater 10 sticks and add them up
you'll have 61 min!!!!!
you'll have 61 min!!!!!
To arrive at the answer provided, you have to make the assumption:
1. That both the sticks have to be completely consumed by the termites.
2. That you do not have any means to measure the sticks.
Without making these assumptions, one can arrive at the following answer:
Let the slow termite eat 10 inches of the 12-inch stick to measure 40 minutes. Remove the slow termite and put the faster termite on to the 16-inch stick and let it eat 7 inches to measure another 21 mintues. This way you can measure 61 minutes.
1. That both the sticks have to be completely consumed by the termites.
2. That you do not have any means to measure the sticks.
Without making these assumptions, one can arrive at the following answer:
Let the slow termite eat 10 inches of the 12-inch stick to measure 40 minutes. Remove the slow termite and put the faster termite on to the 16-inch stick and let it eat 7 inches to measure another 21 mintues. This way you can measure 61 minutes.
I agree with V Bapat... that's how I did it. If I'd known you had to do it that way, I would've done it on paper, instead of mentally... (it woulda been harder, I think..)
Good teaser though ^_-
Good teaser though ^_-
I thought the trick was the other termite could eat one inch in 4 min and that's all. With that interpretation, I gave the slow termite the short stick and let him eat his inch. It then takes the fast termite 33 min to eat the rest for a total of 37 min. I broke the long stick in half and it took the fast termite 24 min to eat one piece for a total of 61. I still have a half a stick left for the slow termite for when he gets hungry again.
good one, i got to the 52 minutes part and then lost my chain of thought and gave up
I would have had the slow termite eat 7 inches and the fast termite eat 10 inches.
I got the solution, but this one took me longer than most. Good teaser!
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