# Tagged Questions

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### 4 crystal balls and a 10,000 story building

There is an analog of this question I've heard with 2 crystal balls but a higher number like 4 or more makes it much more interesting. You are given 4 crystal balls and there is a 10,000 story ...
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### Proof of convergence of Kaprekar's Constant

I've tried googling this one a bit but nothing seems to come up, even though its considered to be a well known fact. Why does the kaprekar process of taking a 4 digit number: L, generating L' and L'' ...
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### An alternating decimal sequence: Does its average have a limit?

Define a sequence of decimals $x_n$ by alternating the digits $1,2,\ldots,n$ left and right, as follows: $$x_1 = .1$$ $$x_2 = .21$$ $$x_3 = .213$$ $$x_4 = .4213$$ $$x_5 = .42135$$ $$x_6 = .642135$$ ...
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### Unbounded sequence with convergent subsequence

I'm just wondering if anyone knows any nice sequences that are unbounded themselves, but have one or more convergent sub-sequences?
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### hand evaluate $\sqrt{e}$

I have seen this question many times as a example of provoking creativity. I wonder how many ways are there to evaluate $\sqrt{e}$ as accurately as possible. The obvious way I can think of is to use ...
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### polynomial series and root multiplicity

Excuse me, because I know this is a double post but I can't for the life of me find the original post. Given a sequence $(a_n)$, one can construct a polynomial of the form ...
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### What is the next number? [closed]

What is the next number in the following set ? $$1,11,21,1211,111221, \ldots$$
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### Sequences, sets and element position in the set.

I have a sequence Q with the length of N. This is the fragment of this sequence: 68 70 72 74 76 78 80 The sequence has been divided into the sets of 4 elements ...
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### Primes created by “n + digital-root(n)” sequences

I've looked at the sequences created by repeatedly adding the digital root of a number to the number until it becomes prime. This is the pseudo-code for the program I've used:   n = 0 ...
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### Next term in the sequence $1, 3, 33, 55, 565, 6567, 8767, …$?

My friend was asked this question at a job interview (it was nothing math related, so I assume it was more of a "let's see how you think" kind of question, not "how well can you identify series") and, ...
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### Limits of infinite processes that terminate in finite time - checking my understanding?

I am a computer scientist by training, but have a fair amount of math background that I've picked up through classes, teaching, and general interest. A student of mine posed a question to me. I think ...
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### Why is 11 times the 7th term of a fibonacci series equal to the sum of 10 terms?

Why is 11 times the 7th term of a fibonacci series equal to the sum of 10 terms? I was watching scam-school on youtube the other day and this number trick just astonished me. Can someone please ...
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### Help explain why (or why not) the solution for a in $\sum_{n=1}^\infty (-1)^n\times(n^{1/n}-a)=0$ is 1-2$C$MRB

$C$MRB is approximately 0.1878596424620671202485179340542732. See this and this. $\sum_{n=1}^\infty (-1)^n\times(n^{1/n}-a)$ is formally convergent only when $a =1$. However, if you extend the ...
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### roulette wheel sequence

Is the sequence of numbers around a European roulette wheel (the integers from 0 to 36 inclusive) random or is there a pattern to it? It is said to have been devised by Pascal, which might be thought ...
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### MRB constant proofs wanted

This article has been edited for a bounty. $C$ MRB, the MRB constant, is defined at http://mathworld.wolfram.com/MRBConstant.html . There is an excellent 56 page paper who's author has passed away. ...
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### Gauss' Summation Trick; Applications and Generalizations

I'm going to write an article about the summation trick attributed to Guass and its applications and generalizations. I'm sure you know what is the trick I mean: $1+2+\cdots+100=101+101+\cdots+101$ ...
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### A binet-like formula for $\small 1 , 2 , 3 , 6 , 9 , 18 , 27, 54, 81, \ldots$?
This is more a "recreational" problem. By another question I came to the question for a closed-form-formula for this sequence $\small 1 , 2 , 3 , 6 , 9 , 18 , 27, \ldots$ which is just the mixture of ...
for any positive number $k$, I have a $(k+1)*(k+1)$ matrix. I wonder if these matrices follow any "obvious" pattern. My goal is to guess the elements for matrix with $k=5$ and above (most probably in ...