# Deceptively Simple Integer Problem

• chillfactor
In summary, the total number of 7's in the given range is 38, not 40. This is because there are 20 7's in the every tenth number group, 8 in the 70's group, and 8 in the 170's group. However, two numbers (77 and 177) are counted twice, giving a total of 38 7's.
chillfactor
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## The Attempt at a Solution

Last edited:
You're forgetting to add 71, 72, 73, ...,76, 78, 79 and 171, 172, 173, ...,176, 178, 179

Well you know that for the hundreds it does not appear once, since the problem does not go up to 700. As for the tens you get all the all the 70's (70 through 79) and all the 170's (170 through 179). As for the ones you get one every 10 digits (7, 17, 27...187, 197).

I do not get why the answer is 38 instead of 40. Like you said, there are 1 7 every 10 numbers, which gives you 20 7's, But if you add 70...79 and 170...179 together, you get 20 more 7's, which gives you a grand total of 40 7's.

morrowcosom said:
Well you know that for the hundreds it does not appear once, since the problem does not go up to 700. As for the tens you get all the all the 70's (70 through 79) and all the 170's (170 through 179). As for the ones you get one every 10 digits (7, 17, 27...187, 197).

I do not get why the answer is 38 instead of 40. Like you said, there are 1 7 every 10 numbers, which gives you 20 7's, But if you add 70...79 and 170...179 together, you get 20 more 7's, which gives you a grand total of 40 7's.
You counted two numbers twice: 77 and 177.

Every tenth number starting with 7: {7, 17, 27, 37, ..., 77, 87, ...,167, 177, 187, 197}
70's group: {70, 71, 72, ... , 76, 77, 78, 79}
170's group: {170, 171, 172, ... , 176, 177, 178, 179}

## What is the "Deceptively Simple Integer Problem"?

The "Deceptively Simple Integer Problem" is a mathematical problem that involves finding the sum of two integers that are seemingly easy to solve, but actually require more complex techniques to accurately determine the solution.

## What makes the "Deceptively Simple Integer Problem" challenging?

The "Deceptively Simple Integer Problem" is challenging because it requires critical thinking and problem-solving skills to identify the underlying complexities and determine the correct solution. It also tests one's ability to think outside the box and not be deceived by the seemingly straightforward nature of the problem.

## What are some common mistakes people make when attempting to solve the "Deceptively Simple Integer Problem"?

Some common mistakes people make when solving the "Deceptively Simple Integer Problem" include assuming that the solution is a single digit number or not considering the order of operations. They may also overlook the possibility of negative numbers or not fully understanding the problem, leading to incorrect calculations.

## Are there any strategies for solving the "Deceptively Simple Integer Problem"?

Yes, there are strategies for solving the "Deceptively Simple Integer Problem." These include carefully reading and understanding the problem, breaking it down into smaller parts, and considering all possible scenarios. Additionally, keeping track of calculations and double-checking answers can help avoid mistakes.

## What real-world applications does the "Deceptively Simple Integer Problem" have?

The "Deceptively Simple Integer Problem" has various real-world applications in fields such as computer science, cryptography, and finance. It can also help improve critical thinking skills and problem-solving abilities, which are valuable in any profession.

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