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Sep 15, 2021 · The phrase "neon number" is sometimes used for a number where: square the number, add the digits of that in base 10, and you get the original number. So, 9 is a neon number (-> 81, 8+1, 9) Indeed it is usually said there are only three neon numbers (0, 1, and 9). Surprisingly I couldn't google any proof of this.
Jan 1, 2018 · The totient of $210$ - the number of values between $1$ and $210$ that are relatively prime to $210$ - is $(2-1)(3-1)(5-1)(7-1)=48$.
Nov 26, 2019 · Eg, $$9 = 4+5 \qquad 40 = 5 + 5 + 5 + 5 + 5 + 5 + 5 +5$$ How many number have this property from 1 to 1000? Multiples of $4$ s and $5$ s are easy, but how do I calculate the number of numbers from different combinations of adding $4$ and $5$? (And which ones are different from multiples of $4$ and $5$?)
Jan 1, 2016 · How many integers between 1000 and 9999 inclusive consist of 2 How many $3$ digit different number that will be divisible by $5$ can be formed from the digit $0,2,3,4,5,6$ lying between $100$ and $1000$.
Apr 12, 2016 · How many integers between $1$ and $1000$ use exactly three digits? The professor shows the solution as: $9 \cdot 9 \cdot 8=648$, but I have no idea where those numbers are coming from. On the other hand, I say that, excluding $1$ to $99$ and $1000$, there are $900$ integers that use exactly three digits.
How many numbers between $1$ and $6042$ (inclusive) are relatively prime to $3780$? Hint: $53$ is a factor. Here the problem is not the solution of the question, because I would simply remove all the multiples of prime factors of $3780$. But I wonder what is the trick associated with the hint and using factor $53$.
Apr 4, 2015 · Let us take the more ideal case of guessing integers between $1$ and $2^{10}-1=1111111111_2$ writing in base $2$ from now on without explicitly writing subscript $2$ each time. Then the algorithm for the guesses will be like this: The initial guess is $1\overline 0$ where $\overline 0$ means fill up with zeros until we have a ten digit number
Aug 7, 2018 · How many $3$ digit different number that will be divisible by $5$ can be formed from the digit $0,2,3,4,5,6$ lying between $100$ and $1000$. 2 How many odd $100$-digit numbers such that every two consecutive digits differ by exactly 2 are there?
How many positive integers less than 1,000 are multiples of 5 and are equal to 3 times an even integer? So, multiples of 5 include: 5, 10, 15, 20, 25, 30, 35, ..., 990, 995, 1000. But there's another condition and we need to remove some of these multiples of 5. We need multiples of 5 that are also thrice an even integer. So we need multiples of ...
Mar 19, 2016 · $\begingroup$ Total ways are $1000^{1000}$ . and specific number has $1000$ ways so its almost 0 in 1 time $\endgroup$ – Archis Welankar Commented Mar 19, 2016 at 14:52
