### Questions (45)

 10 Subset of knight's move in chess. 7 Prove that $2^{30}$ has at least two repeated digits. 4 Is it possible to start with a knight at some corner of a chess board and reach the opposite corner passing once through all the squares? 4 Find the smallest positive integer such that $S(n)=10, S(n^2)=100$. 4 Factorials and prime numbers

### Reputation (497)

 +15 Let the rational number $p/q$ be closest to but not equal to $22/7$ among all rational numbers with denominator $< 100$. +15 Integrate $\int_0^\infty e^{-t}|x-t|dt$. +10 Suppose z is any root of $11z^8 + 20 iz^7 + 10iz –22 = 0$. Then $S = |z|^2+| z|+ 1$ satisfies? +5 The maximum possible area bounded by the parabola $y = x^2 + x + 10$ and a chord of the parabola of length $1$ is?

 1 find area of kite given side length 1 An elementary sequence problem 0 Deleting digits

### Tags (56)

 1 elementary-number-theory × 10 1 sequences-and-series 1 circles × 5 0 number-theory × 13 1 algebra-precalculus × 4 0 divisibility × 6 1 area × 2 0 combinatorics × 5 1 tangent-line 0 square-numbers × 4

### Accounts (11)

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