45 $55$ gangsters shoot the nearest gangster to them, where all the distances between them are different. Prove that at least one gangster will survive. 33 Using the Left-Inverse to “Solve” an Impossible System of Equations 30 Integral of a function's derivative does not equal the original function? 19 Total distance traveled when visiting all rational numbers 17 Number of total possibilities for an equation

### Reputation (17,871)

 +40 Two conflicting views on $1_{[n,n+1]}$ +25 Combined variation with four variables: Is this even possible to solve? +25 Finding Parameters to Minimize a Maximum of Multiple Functions +15 Given $A=\alpha + M$ and $B = \beta + M$, show that either $A=B$ or $A\cap B = \varnothing$.

### Questions (10)

 5 Least number of rounds to find all hidden pairs 5 For all $x\in\mathbb{N}^*$ there is some $y\in\mathbb{N}^*$ such that $xy$ contains only $0$s and $1$s. 5 Evaluate the sum $\sum_{i=0}^{n} (-1)^{n-i} \binom{n}{i} f(i)$ 2 Combinatorial identity on partitions 2 Maximizing Stirling numbers of the second kind

### Tags (346)

 203 real-analysis × 114 97 probability × 58 181 linear-algebra × 95 82 limits × 48 173 calculus × 101 76 integration × 27 153 combinatorics × 62 62 puzzle × 7 123 sequences-and-series × 55 51 algebra-precalculus × 28