Marcus Chen
A popular riddle asks: John has been hired to paint the numbers 1 through 100 on 100 apartments. How many times will he have to paint the number 8? The answer is 20 times. The number 8 appears 10 times in the units position (8, 18, 28, 38, 48, 58, 68, 78, 88, 98) and 10 times in the tens position (80, 81, 82, 83, 84, 85, 86, 87, 88, 89).
| Characteristics | Values |
|---|---|
| Name of the person | Tom/John |
| Task | Paint the number of plates on 100 apartments |
| Total numbers to be painted | 1 through 100 |
| Number of times the digit 8 is painted | 20 |
| List of numbers with 8 in them | 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88 (8 twice), 89, 98 |
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What You'll Learn
The riddle: John paints numbers 1-100 on 100 apartments
John has been hired to paint the numbers 1 through 100 on 100 apartments. How many times will he have to paint the number 8?
This riddle has sparked a lot of debate, with several interpretations and answers being offered. Some argue that the answer is 20, as there are 20 unique numbers between 1 and 100 that include the digit 8. These numbers are: 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, and 98.
Another interpretation of the riddle leads to an answer of 2,000. This assumes that John paints every number from 1 to 100 on each of the 100 apartments. In this case, he paints the digit 8 a total of 20 times on each apartment, resulting in painting it 2,000 times overall.
A more unconventional interpretation of the riddle suggests that the answer is 0 or 1. This interpretation assumes that John is painting "1-100" on each door, rather than the individual numbers from 1 to 100. In this case, he wouldn't paint the number 8 at all, leading to an answer of 0. Alternatively, some argue that he only paints the "number" 8 once, as 18 and 88 are not the same, resulting in an answer of 1.
The most commonly accepted answers are 20 and 2,000, depending on how the riddle is interpreted. It's important to carefully consider the wording of the riddle and the specific instructions given to John to determine the correct answer.
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The digit 8 is painted 20 times
The number 8 is an element of the set of numbers from 1 to 100. To determine the number of times the digit 8 is painted, we need to find the cardinality of the subset T of S that consists of all the numbers in S that contain the digit 8.
The numbers that contain the digit 8 and will be painted are: 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88 (which has two 8s), 89, and 98.
Therefore, the digit 8 is painted a total of 20 times.
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The number 8 is painted twice in '88'
The riddle, "How many times does he have to paint the number 8?", is an interesting brainteaser. The answer is 20 times, and this includes the number 88, where the digit 8 is painted twice.
The riddle is based on a scenario where someone is tasked with painting the numbers 1 through 100 on 100 apartments. This means that they will have to paint the number 8 a total of 20 times, including the two 8s in 88.
The numbers that contain the digit 8 and would need to be painted are: 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, and 98. Therefore, the digit 8 is painted a total of 20 times, including the two 8s in the number 88.
It's important to note that this riddle assumes that the digit 8 is only counted when it is painted as part of a number and not as part of a word or other form of representation. Additionally, the riddle specifies that the numbers are being painted on apartments, which helps to clarify that each number is only being painted once per apartment, rather than repeating the sequence 1 to 100 on each apartment.
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The number 8 is painted 10 times in the 81-89 series
The number 8 is a unique digit. It is the only number that, when written, remains the same even when it is turned on its side. This might be why Tom, who has been tasked with painting the number of plates on 100 apartments, will have to paint the number 8 a total of 20 times.
However, in the 81-89 series, the number 8 is painted 10 times. This is because the number 8 is written twice in the number 88. If we count the number of times the digit 8 is painted in the series 81-89, it only amounts to 10.
This riddle is a great example of how careful thinking and number sense are required to solve a simple-looking question. It is also a reminder to pay close attention to the wording of a problem. The distinction between the number of times the digit 8 is painted and the number of times the number 8 is painted is an important one.
The answer to the riddle, therefore, depends on whether we are counting the digit 8 or the number 8. If we are counting the digit 8, then the answer is 10 in the 81-89 series. If we are counting the number 8, then the answer is 20 in the full series of 1-100.
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The answer is not 19, 11 or 1900
The correct answer to the riddle is 20. The riddle asks how many times Tom will have to paint the number 8 if he is painting the numbers 1 through 100 on 100 apartments. The number 8 appears 20 times in the numbers 1 through 100: 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88 (8 twice), 89, and 98.
If your answer is 19, you might have missed the number 88, where 8 is painted twice. If your answer is 11, you might have missed the series from 81 to 89, where 8 appears 10 times, or you might have only counted the digit 8 once. If your answer is 1900, you might have misunderstood the puzzle; John is painting the numbers 1 through 100 on 100 different apartments, not 100 times on one apartment.
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Frequently asked questions
Tom will have to paint the number 8 a total of 20 times.
By listing out the numbers 1 through 100, we can count the number of times the digit 8 appears: 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88 (8 twice), 89, 98.
Yes, you can think of the numbers in two groups: those with 8 in the units position (10 numbers: 8, 18, 28, ... , 88, 98) and those with 8 in the tens position (also 10 numbers: 80, 81, 82, ..., 88, 89).
In this case, the answer would be 19, as the digit 8 is painted twice in the number 88.
