Tom's Many Painted Eights

how many times did tom paint the number 8

The riddle, How many times did Tom paint the number 8? has gained popularity during the COVID-19 pandemic. In the riddle, Tom is hired to paint the numbers from 1-100 on the doors of a new hotel with 100 rooms. The answer to this riddle is debated. Some argue that Tom painted the number 8 twenty times, while others argue that he painted it 2,000 times, and some even argue that the answer is 0 or 1.

Characteristics Values
Number of times Tom painted 8 on each door 20
Total number of doors 100
Total number of times Tom painted 8 2,000
Alternative answers 0, 1

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Tom paints 1-100 on each door: 2,000 eights

The riddle "Tom paints 1-100 on each door: 2,000 eights" has gained popularity, especially during the coronavirus outbreak. The riddle goes as follows: "In a new hotel containing 100 rooms, Tom was hired to paint the numbers from 1-100 on the doors. How many times will Tom have to paint the number 8?"

The answer to this riddle is debated. Some interpret the riddle to mean that Tom painted each door with the numbers 1-100, which would mean he painted the digit "8" 20 times on each door, for a total of 2,000 times. This interpretation assumes that Tom painted the following numbers with "8" in them on all 100 doors: 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, and 98. This interpretation acknowledges that the number 88 counts as painting "8" twice.

However, others argue that the answer is 0 or 1 if the riddle is worded differently, leaving out the word "from" in the question. In this case, Tom is painting "1-100" on all 100 doors, so he never paints the digit "8." Some people who interpret the riddle this way argue that Tom only painted the "number" 8 once, even though he painted the "digit" 8 multiple times within other numbers.

The interpretation that Tom painted each door with the numbers 1-100, resulting in 2,000 eights, aligns with the provided answer to the riddle. However, it's important to acknowledge that different interpretations of the riddle's wording can lead to alternative answers.

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Tom paints one number per door: 20 eights

Tom has been hired to paint the numbers from 1 to 100 on the doors of a new hotel with 100 rooms. The answer to the riddle, "How many times did Tom paint the number eight?" depends on how the question is interpreted.

If we assume that Tom painted one number per door, he would have painted the number 8 twenty times. The ten 8s in the units position (8, 18, 28, etc.) and the ten 8s in the tens position (80, 81, 82, etc.). This interpretation assumes that the riddle is asking about the digit 8 and not the number as a whole.

However, if we interpret the riddle to mean that Tom painted all the numbers from 1 to 100 on each door, then he would have painted the number 8 two thousand times. This is because he painted all one hundred doors with the numbers 1 to 100, which include twenty 8s, as mentioned earlier.

The phrasing of the riddle is crucial to determining the answer. If the question is worded without the word "from," it could be interpreted that Tom painted "1-100" on each door, in which case the answer would be zero, as he never painted the number 8. Alternatively, some argue that the answer is one because the riddle specifically asks about the "number" 8, which is unique from the "digit" 8.

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Tom paints 1-100 on some doors: 20 eights

The riddle of Tom painting the numbers 1-100 on 100 doors has gained some popularity during the coronavirus outbreak. The question is usually presented as follows: "In a new hotel containing 100 rooms, Tom was hired to paint the numbers from 1-100 on the doors. How many times will Tom have to paint the number 8?"

The answer to this riddle is debated. Some argue that the answer is 20, as there are 20 unique numbers that contain the digit 8 between 1 and 100. These numbers are: 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, and 98. In the case of 88, Tom would have to paint the digit 8 twice, so that's 19 numbers with the digit 8, plus one more 8 in the number 8 itself, making 20 in total.

However, the question implies that Tom is painting every number from 1-100 on each door. If that is the case, then he paints the digit 8 2,000 times (20 unique numbers containing 8, painted on 100 doors).

Another interpretation of the riddle is that Tom is painting "1-100" on each door, in which case the answer would be 0, as he never paints the number 8. Some even argue that the answer is 1, as 8 is a unique number and numbers like 18 and 88 are not the same.

Therefore, the answer to the riddle depends on the specific interpretation of the question and the assumptions made about how Tom is painting the numbers on the doors.

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Tom paints 1-100, not from 1-100: 0 eights

The riddle, "Tom paints 1-100, not from 1-100: 0 eights", is a play on words. The phrasing of the riddle is crucial to its interpretation. The answer to the riddle is 0 because, by removing the word "from", the question becomes ambiguous. It could be interpreted as Tom painting the sequence "1-100" on each door, in which case he wouldn't paint any eights.

The original riddle, which includes the word "from", implies that Tom is painting every number from 1 to 100 on each door. In this case, he would indeed paint the number eight. The numbers eight, eighteen, twenty-eight, and so on, up to ninety-eight, all contain the digit eight. Additionally, the number eighty-eight has two eights, so it counts as painting eight twice. Thus, Tom paints the digit eight twenty times on each door, for a total of one hundred doors. This means that Tom paints the digit eight two thousand times overall.

However, the modified riddle without the word "from" can be interpreted differently. By removing "from", the question becomes open to the interpretation that Tom is painting the sequence "1-100" on each door, rather than every number from 1 to 100. In this case, he would not paint any eights, hence the answer of zero.

The phrasing of the riddle is crucial to its interpretation and the resulting answer. The original riddle with the word "from" implies that Tom paints each number from 1 to 100 on every door, resulting in him painting the digit eight two thousand times. However, the modified riddle without "from" can be understood as Tom painting the sequence "1-100", leading to an answer of zero eights.

In conclusion, the riddle "Tom paints 1-100, not from 1-100: 0 eights" is a wordplay that hinges on the absence of the word "from". This subtle change in wording alters the interpretation of the question and leads to the answer of zero eights painted by Tom.

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Tom paints 1-100, excluding 8-variants: 1 eight

The answer to this riddle is the subject of some debate. The question is often posed as follows:

> In a new hotel containing 100 rooms, Tom was hired to paint the numbers from 1-100 on the doors. How many times will Tom have to paint the number 8?

Some people interpret the question to mean that Tom paints every number from 1-100 on each door. Under this interpretation, Tom paints the number 8 two thousand times (20 times on each of the 100 doors).

However, others argue that the question implies that Tom paints one number per door, from 1 to 100. Under this interpretation, Tom paints the number 8 twenty times (on doors 8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 98).

A third interpretation is that Tom is painting "1-100" or "the numbers 1-100" on all 100 doors, so he never paints "8" at all.

Finally, some argue that Tom only paints the "number" 8 once, even if he paints the "digit" 8 multiple times, because numbers like 18 and 88 are not the same as the number 8.

For the purposes of this answer, let's assume that Tom paints one number per door, from 1 to 100, excluding 8-variants: 1 eight. Under this interpretation, Tom paints the number 8 once.

Frequently asked questions

Tom was hired to paint the numbers from 1-100 on the doors of 100 rooms in a hotel.

There are different interpretations of the riddle. If we assume Tom painted every number from 1-100 on each door, the answer is 2,000 (20 times on each of the 100 doors). If we assume Tom painted one number per door, the answer is 20.

8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88 (8 twice), 89, and 98.

To calculate the number of times Tom painted 8, we need to determine the cardinality of the subset of numbers from 1 to 100 that contain the digit 8.

Yes, some people argue that the answer is 0 if the riddle is worded without the word "from," implying that Tom painted "1-100" on each door. Others argue the answer is 1 because the riddle asks specifically about the "number" 8, which is a unique number, and numbers like 18 and 88 are not the same.

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