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question:A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?
answer:To solve this problem, let's break it down step by step. The snail climbs 3 feet during the day but slips back 2 feet at night, which means it effectively moves 1 foot up each day. However, when the snail is close to the top of the well, this pattern changes slightly. If the snail climbs 3 feet during the day and reaches or surpasses the top of the 20-foot well, it won't slip back at night since it has already escaped the well. To determine the number of days, we can calculate how many days it takes the snail to climb 18 feet, as on the 18th foot, the next day it will climb 3 feet and reach 21 feet, thus escaping the well. Since the snail effectively moves 1 foot up each day, it will take 18 days to reach 18 feet. On the 19th day, when the snail climbs 3 feet, it will reach 21 feet and be out of the well. Therefore, it will take 18 days for the snail to climb 18 feet and the 19th day to climb the final 3 feet and escape, resulting in a total of 18 + 1 = 19 days for the snail to reach the top and escape the well.
question:The bat and ball problem is a classic logical reasoning puzzle. It goes like this: A bat and a ball together cost 1.10. The bat costs 1.00 more than the ball. How much does the ball cost?
answer:This classic puzzle is a great example of a simple yet tricky problem that requires careful consideration. To solve this problem, let's break it down step by step. We know that the bat and the ball together cost 1.10. We also know that the bat costs 1.00 more than the ball. Let's denote the cost of the ball as x. Since the bat costs 1.00 more than the ball, the cost of the bat is x + 1.00. The total cost of both the bat and the ball together is 1.10. We can set up an equation to represent this: x + (x + 1.00) = 1.10 Combine the like terms: 2x + 1.00 = 1.10 Subtract 1.00 from both sides: 2x = 0.10 Divide both sides by 2: x = 0.05 Therefore, the ball costs 0.05.
question:Explain in your own words why some people might get this wrong when presented with this question.
answer:When presented with the bat and ball problem, some people might get it wrong because of an intuitive but incorrect assumption. The problem states that the bat costs 1.00 more than the ball, and the total cost of both is 1.10. A common mistake is to immediately assume that the bat costs 1.00 and the ball costs 0.10, as this seems like a straightforward and obvious solution. However, this assumption is incorrect. This mistake occurs because people tend to focus on the 1.00 difference between the bat and the ball, and incorrectly conclude that the bat must cost 1.00. This then leads them to allocate the remaining 0.10 to the ball. The problem is that this approach ignores the fact that the bat costs 1.00 more than the ball, not that the bat costs 1.00. In other words, people may be misled by the dollar amounts mentioned in the problem and fail to properly consider the relationship between the costs of the bat and the ball. This results in a failure to set up the correct equation, leading to an incorrect conclusion. The correct solution requires a more careful and systematic approach, where the relationship between the costs is explicitly considered.
question:CoT: Excalibur is a topic of interest of many in different varying of fields all over the world. Answer: yes What is the question? This is the question: Yes / no, is the following a verifiable fact? Excalibur inspired many to learn more about myths. CoT: Sand has a functionality as a building material and has been used for centuries. Answer: yes What is the question? This is the question: Is the following statement true? Sand aids building structures by creating a firm, and level base for projects' bases. CoT: Cloris Leachman was an actress who played a character in a show who had premonitions. Answer: no What is the question? This is the question: Is the following sentence factually correct? Cloris Leachman had many of premonitions. Options: - yes - no CoT: It's a fact that Sonic runs extremely fast in his games. Answer: yes
answer:What is the question? This is the question: Is the following statement true? Sonic the Hedgehog is known for his incredible speed in his video games. Options: - yes - no