List questions from problem-solving

Published on 04 Mar 2020 - 15:22

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IMO 2019: Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(2a) + 2\, f(b) = f \big( f (a+b)\big)$.

Published on 29 Mar 2026 - 19:14

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Can a 7-sided die be simulated by rolling two 5-sided dice, discarding and re-rolling when their total exceeds $7$?

Published on 28 Mar 2026 - 12:32

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If $f\big(f(x)\big)=2^x-1$ for every $x\in\mathbb{R}$, then what is $f(0)+f(1)$?

Published on 30 Mar 2026 - 0:04

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Number Theory Problem Germany 2003

Published on 25 Mar 2026 - 15:44

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Prove: $\frac{a}{a^2+b^3+c^3}+\frac{b}{b^2+c^3+a^3}+\frac{c}{c^2+a^3+b^3}\leq \frac{1}{5abc}$ for $a+b+c=1$.

Published on 06 Mar 2020 - 16:57

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Problem filling the board with a set of numbers

Published on 29 Mar 2026 - 12:30

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Solvability condition for diophantine equations

Published on 07 Mar 2020 - 10:33

56

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Show that the function $d$ defines a metric on $\mathbb Z$.

Published on 08 Mar 2020 - 4:49

162

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How would you formulate this graph problem?

Published on 08 Mar 2020 - 6:47

49

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inner product space operations(proving polar coordinates)

Published on 09 Mar 2020 - 17:41

991

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Motel Probability and Combinatorics Questions

Published on 10 Mar 2020 - 7:16

53

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What is the problem with this differential equation?

Published on 10 Mar 2020 - 14:14

43

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Abou independent random variables

Published on 11 Mar 2020 - 0:38

30

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multiply sample space coin flipping

Published on 11 Mar 2020 - 13:00

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Distributing $k$ objects in $n$ boxes vs. how many 4 letter words can we make?

IMO 2019: Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(2a) + 2\, f(b) = f \big( f (a+b)\big)$.

Can a 7-sided die be simulated by rolling two 5-sided dice, discarding and re-rolling when their total exceeds $7$?

If $f\big(f(x)\big)=2^x-1$ for every $x\in\mathbb{R}$, then what is $f(0)+f(1)$?

Number Theory Problem Germany 2003

Prove: $\frac{a}{a^2+b^3+c^3}+\frac{b}{b^2+c^3+a^3}+\frac{c}{c^2+a^3+b^3}\leq \frac{1}{5abc}$ for $a+b+c=1$.

Problem filling the board with a set of numbers

Solvability condition for diophantine equations

Show that the function $d$ defines a metric on $\mathbb Z$.

How would you formulate this graph problem?

inner product space operations(proving polar coordinates)

Motel Probability and Combinatorics Questions

What is the problem with this differential equation?

Abou independent random variables

multiply sample space coin flipping

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