# All Questions

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### the probability that there will be exactly two men between A and B?

If six men, among whom are A and B, stand in a circle, what is the probability that there will be exactly two men between A and B?
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### Proving if function is one to one?

f : (N × N) → N defined as: f(x, y) = [((x + y)(x + y + 1))/2] + y I know that f(x,y) = f(x',y') in order to be a one to one. So it'll be : ...
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### equivalent of a $\mathrm{diag}(S)$ in matrix notation

Suppose I have a symmetric matrix $S\in\mathbb{R}^{n\times n}$ (positive semidefinite if this helps). Is there a way to write the transformation $\mathrm{diag}(S)$ using standard linear algebra ...
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### Decreasing by $\sqrt{n}$ every time
We start with a number $n>1$. Every time, when we have a number $t$ left, we replace it by $t-\sqrt{t}$. How many times (asymptotically, in terms of $n$) do we need to do this until our number gets ...
### Proof that max value of $n$-bit binary number is $2^n - 1$
After reading this programming question , I wanted to prove the assertion. I'm wondering whether the below would be considered a complete and clear proof. Claim: $\sum_{i=0}^{n-1} 2^i = 2^n - 1.$ ...