Tyler Brooks
This brainteaser has been used in interviews for companies such as Microsoft and IBM. The puzzle is as follows: you have two candles, each of which burns for one hour. You also have a box of matches. How can you measure exactly 45 minutes?
| Characteristics | Values |
|---|---|
| Number of candles | 2 |
| Burn time of each candle | 60 minutes |
| First step | Light both ends of the first candle and one end of the second candle |
| Second step | Light the other end of the second candle when the first candle burns out |
| Total time elapsed | 45 minutes |
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What You'll Learn
Light both ends of one candle and one end of the other
To measure 45 minutes using two candles, you can employ a clever trick that involves lighting both ends of one candle and only one end of the other. Here's a step-by-step guide on how to do it:
Step 1: Prepare the Candles
Start by placing the two candles on a flat, horizontal surface, ensuring they are identical in length and thickness. Position them side by side, with their ends aligned.
Step 2: Light the Candles
Take a matchstick or a lighter and light both ends of one candle. Simultaneously, light only one end of the second candle. This is the key step in measuring 45 minutes.
Step 3: Observe the First Candle
The first candle, with both ends lit, will burn down in 30 minutes. This is because lighting both ends effectively halves the burn time of that candle.
Step 4: Light the Other End of the Second Candle
Once the first candle has completely burned down, use your matchstick or lighter to ignite the unlit end of the second candle. At this point, the second candle has been burning from one end for 30 minutes and has 30 minutes of burn time remaining.
Step 5: Observe the Second Candle
Since the second candle now has both ends lit, it will take only 15 minutes to completely burn down. This is because lighting both ends causes the candle to burn twice as fast.
In total, the process takes 30 minutes from the first candle and 15 minutes from the second candle, resulting in a cumulative burn time of 45 minutes. This method assumes that the candles burn at a consistent rate and that external factors like airflow or drafts do not significantly affect the burn time.
This candle trick is a classic brainteaser often used in interviews and puzzles to test logical and analytical thinking skills. It's a fascinating demonstration of how creative thinking can solve unique time-measurement challenges.
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When the first candle burns out, light both ends of the second candle
To measure 45 minutes using two candles, each of which takes an hour to burn, follow these steps:
Firstly, light both ends of the first candle and one end of the second candle. The first candle will burn out in 30 minutes as lighting it from both ends will cause it to burn twice as fast. At this point, the second candle will have burnt halfway.
When the first candle burns out, light the unlit end of the second candle. As the second candle is now burning from both ends, it will take another 15 minutes for it to burn out.
Thus, by the time the second candle is completely burnt out, a total of 45 minutes will have elapsed (30 + 15 = 45 minutes). This solution assumes that the candles burn at a consistent rate and that the rate of burning is not affected by factors such as airflow or the orientation of the candle.
It is important to note that this problem assumes that the candles burn uniformly, meaning that lighting a candle from both ends will cause it to burn in exactly half the time. In reality, candles may burn unevenly, with one end burning faster than the other, which would affect the accuracy of this method.
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The second candle will burn out in 15 minutes
To measure 45 minutes using two candles, each of which takes an hour to burn, you must follow a precise sequence of steps. Firstly, lay the candles on a horizontal surface, ensuring they are positioned next to each other but pointing in opposite directions. This setup is crucial for accurate timing. Light both candles from one end. When the first candle burns out, exactly 30 minutes will have passed. At this point, light the unlit end of the second candle. As it burns from both ends, the second candle will only last for 15 minutes, giving you a total elapsed time of 45 minutes (30 + 15).
This solution assumes that the candles burn at a consistent rate, regardless of their orientation. By lighting one candle from both ends, it will burn twice as fast and last for only 30 minutes instead of the full hour. Once the first candle has burned out, lighting the second candle from both ends will cause it to burn faster and last for just 15 minutes.
The key to success with this method is careful observation and timing. You must pay close attention to the candles as they burn and be ready to light the second candle from the other end as soon as the first one goes out. This technique relies on the principle of using the candles' burning rates to measure time accurately.
It's important to note that this solution is based on the assumption that the candles burn uniformly and consistently. In reality, candles may burn unevenly, affecting the accuracy of the timing. However, with careful observation and quick reactions, this method can provide a reasonably reliable way to measure 45 minutes using only two candles.
This problem showcases the creative thinking and problem-solving skills often sought in interviews for tech giants like Microsoft and IBM. It challenges individuals to think outside the box and apply logical reasoning to a unique situation. By understanding the properties of the candles and their burning rates, a solution can be devised to measure a specific duration accurately.
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The total time elapsed is 30 + 15 = 45 minutes
This is a famous Microsoft interview question. You have two candles, each of which burns for one hour. They burn unevenly, and you also have a box of matches. You need to measure 45 minutes.
Here's how you can do it:
Firstly, light one candle from both sides and the second candle from one side. The first candle will burn out in 30 minutes, and the second candle will be burnt halfway.
Now, light the second candle from both sides. It will finish in the next 15 minutes. So, in total, you have calculated 45 minutes.
The key here is that lighting a candle from both sides will cause it to burn out in half the time, i.e., 30 minutes. This allows you to use the candles to measure time in increments of 30 minutes. By lighting one candle from both sides and the other from one side, you can time 30 minutes. Then, by lighting the second candle from both sides, you add another 15 minutes, giving you a total of 45 minutes.
This solution assumes that the candles burn at a consistent rate and that their orientation (horizontal or vertical) does not affect their burn rate.
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This assumes a consistent burn rate
This solution assumes a consistent burn rate for the candles. To measure 45 minutes using two candles, each of which burns for one hour, follow these steps:
Firstly, place the candles on a horizontal surface, ensuring they are secure and level. Next, light both ends of the first candle and only one end of the second candle. Since the candles burn uniformly, lighting a candle from both ends will cause it to burn in half the time, so 30 minutes.
Once the first candle has burned out, light the other end of the second candle. As before, the candle will burn in half the time, so 15 minutes. Therefore, when the second candle burns out, a total of 45 minutes will have elapsed.
This solution relies on the principle of adjusting the burn rate of the candles by lighting multiple ends. By lighting two ends of a candle, the effective burn time is halved. This allows for the precise measurement of 45 minutes, despite the candles only burning for a full hour under normal circumstances.
It is important to note that this solution assumes that the candles will burn at a consistent rate throughout. Any variations in burn rate, such as changes caused by drafts or differences in wax density, could affect the accuracy of the timing. Therefore, this solution is based on ideal conditions, and in practice, the actual time elapsed may vary slightly.
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Frequently asked questions
Light both ends of one candle and one end of the other candle. When the first candle burns out in 30 minutes, light the other end of the second candle. It will finish in the next 15 minutes, giving you a total of 45 minutes.
The solution assumes that the rate at which the candles burn does not change with respect to its orientation—horizontal or vertical.
Yes, lay both candles on a horizontal surface, next to each other, but pointing in opposite directions. Light both candles and wait until their flames meet—30 minutes will have passed. Now rearrange the candles so that they point in the same direction and wait until the flames meet—this will take another 15 minutes.
Yes, one variation of the previous method involves lighting one candle and using the other candle as a reference. When the first candle burns to half the length of the reference candle, light the other candle from one end. When the second candle burns out completely, 45 minutes will have passed.
