Olympiades ENSAE - 1er S 2025

  • Posted on: 8 May 2025
  • By: sbana

Exercice 1

Cet exercice est composé de parties $A$, $B$ et $C$  dans une large mesure indépendantes.
 
Partie A :

On définit par $A$ l'ensemble des fonctions $f\ :\  [0\;,1]\rightarrow \mathbb{R}$ vérifiant les conditions suivantes :

$\bullet\ $Pour tous réels $\alpha$ et $\beta\in[0\;,1]/\alpha <\beta$ si $f(\alpha)\times f(\beta)\leq 0$ alors il existe au moins $\overline{x}]\alpha\;,\beta[$ tel que $f\left(\overline{x}\right)=0$

$\bullet\ f(x)=f(1)=0$

$\bullet\ $Pour tout $x$ réel de l'intervalle $\left[0\;,\dfrac{7}{10}\right]\;,f\left(x+\dfrac{3}{10}\right)\neq f(x)$

Soit $f$ un élément de $A.$

On définit une fonction $h\ :\ \left[0\;,\dfrac{7}{10}\right]\rightarrow\;,\mathbb{R}$ donnée par : $h(x)=f\left(x+\dfrac{3}{10}\right)-f(x)$, pour tout $x\left[0\;,\dfrac{7}{10}\right]$

On suppose que h vérifie la condition $(1)$
 
$(1)$ Montrer que $h(x)$ est de signe constant sur $[0\;,\dfrac{7}{10}]$

$(2)$ Démontrer que l'équation $f(x)=0$ admet au moins sept solutions sur $[0\;,\dfrac{7}{10}]$
 
Partie B :

Les martiens sont les habitants, en nombre éventuellement infini, de la planète Mars.

Vis à vis d'eux-mêmes et de leurs semblables, les martiens sont capables de ressentir deux types d'émotions, qu'ils appellent amour et respect.

Il a été observé que :  

$\bullet\ $Chaque martien aime un et un seul martien, et respecte un et un seul martien.
 
$\bullet\ $Si $A$ aime $B$, alors tout martien qui respecte $A$ aime également $B$
 
$\bullet\ $ Si $A$ respecte $B$, alors tout martien qui aime $A$ respecte également $B.$
 
$\bullet\ $Chaque martien est aimé d'au moins un martien.  

On se propose de vérifier s'il est vrai que chaque martien respecte le martien qu'il aime.
 
Pour chaque martien $x$ , on désigne respectivement par $f(x)$ et $g(x)$ les martiens aimés et respectés par $x$

$(1)$ Montrer que les fonctions $f$ et $g$ sont bien définies de l'ensemble $X$ des martiens sur lui-même.
 
$(2)$ Montrer que $f[g(x)]=f(x)$ et $g[f(x)]=g(x)$ pour tout $x$ dans $X$
 
$(3)$ Montrer finalement que, pour tout $x$, on a $f(x)=g(x)=x$
 
$(4)$ Conclure !

Partie C :

Soit $n\in\mathbb{N}^{\ast}$, $m_{1}$, $m_{2}$, $\ldots$, $m_{n}$ des réels et $\mathrm{e}_{1}$, $\mathrm{e}_{2}$, $\ldots$, $\mathrm{e}_{n}$

des réels strictement, positifs on a :
$$\begin{array}{rcl}\dfrac{m_{1}^{2}}{\mathrm{e}_{1}}+\dfrac{m_{2}^{2}}{\mathrm{e}_{2}}+\ldots+\dfrac{m_{n}^{2}}{\mathrm{e}_{2}}\geq\dfrac{\left(m_{1}+m_{2}+\ldots+m_{n}\right)^{2}}{\mathrm{e}_{1}+\mathrm{2}+\ldots+\mathrm{e}_{n}}\end{array}$$

Cette inégalité est connue sous le nom de l'inégalité des Mauvais Élèves $(IME)$
En appliquant l'$IME$, montrer que :

$(1)$ Si $a_{1}$, $a_{2}$, $\ldots$, $a_{n}$ sont $n$ réels strictement positifs alors :

$\dfrac{1}{a_{1}}+\dfrac{1}{a_{2}}+\ldots+\dfrac{1}{a_{n}}\geq\dfrac{n^{2}}{a_{1}+a_{2}+\ldots+a_{n}}$
 
$(2)$ Si $a$, $b$ et $c$ sont $3$ réels strictement positifs alors :

$\dfrac{a}{a+2c}+\dfrac{b}{b+2a}+\dfrac{c}{c+2b}\geq 1$

$(3)$ Si $x$, $y$ et $z$ sont réels strictement positifs tels que : $\dfrac{1}{x+1}+\dfrac{1}{y+1}+\dfrac{1}{z+1}=1$ alors $xyz\geq 8$

On considère la figure suivante où $ABMN$ et $ARSC$ sont des carrés construits à partir du triangle $ABC$

On construit en outre le parallélogramme $ANA'R$

1. a. Démontrer que $\left(AA'\right)$ est une hauteur du triangle $ABC$

b. Démontrer que $AA'=BC$

2. On considère les parallélogramme $NARA'$, $QBMB'$ et $SCPC'$

Justifier que $\left(AA'\right)$, $\left(BB'\right)$ et $\left(CC'\right)$ sont concourantes.

b. Démontrer que dans un triangle $ABC$, si $M$ désigne le milieu de $[BC]$ alors : $AB^{2}+ac^{2}=2\left(BM^{2}+AM^{2}\right)$ (Théorème d'Apollonius).

c. En déduire que $NR^{2}+QM^{2}+SP^{2}=3\left(AB^{2}+AC^{2}+BC^{2}\right)$

Exercice 3

$\mathbb{R}$ désigne l'ensemble des nombres réels.

Dans ce problème, on cherche à déterminer les applications $f$ définies sur $]0\ ;\ +\infty[$ et à valeurs dans $]0\ ;\ +\infty[$  vérifiant les deux propriétés suivantes :

$\bullet\ $pour tous nombres réels strictement positifs $x$ et $y$, $f[xf(y)]=yf(x)$ ;
 
$\bullet\ f$ est bornée sur $[1\ ;\ +\infty[$ il existe un nombre réel $A$ tel que pour tout nombre réel $x\geq 1$, $f|f(x)|\leq A$

Partie I

Soit $I$ un intervalle de $\mathbb{R}$ et soit $h$ une application définie sur $I$ et à valeurs dans $I$

On dit que est $h$ une involution de $I$ si pour tout nombre réel $x$ dans $I\;,h[h(x)]=x$

1. Donner un exemple d'involution de $\mathbb{R}$ dans R autre que l'identité.

2. Donner un exemple d'involution de $]0\ ;\ +\infty[$ dans $]0\ ;\ +\infty[$ autre que l'identité.   

3. Montrer qu'une involution de $I$ dans $I$ est bijective.

Partie II

Soit $f$ une fonction vérifiant les deux conditions citées au début de l'énoncé.
 
1. Soit deux nombres réels $y_{1}$, $y_{2}$ strictement positifs tels que $f\left(y_{1}\right)=f\left(y_{2}\right).$

Montrer que $y_{1}f(1)=y_{2}f(1)$

2. Montrer que $f$ est injective.
 
3. Montrer que $f[f(1)]=f(1)$ puis $f(1)$ puis que $f(1)=1$
 
4. Montrer que $f$ est une involution de $]0\ ;\ +\infty[$

5. Soient $a$ et $b$ deux réels strictement positifs.

Montrer que $f(ab)=ff(a)f(b)$

Indication : on pourra poser $b=f(y)$

Partie III

On note $F$ l'ensemble des points fixes de $f$ : $F=\lbrace x\in]0\ ;\`+\infty\left[/f(x)=x\right\rbrace$
 
1) Montrer que pour tout $x\in]0\ ;\ +\infty[\;,xf(x)$ est un élément de  $F.$

2. Montrer que $1$ est un élément de $F.$
 
3. Montrer que si $x$ et $y$ sont des éléments de $F$, alors $xy$ et $\dfrac{x}{y}$
 sont également des éléments de $F.$
 
4. Montrer que si $x$ est un élément de $F$, alors pour tout entier naturel $n$, $xn$ est un élément de $F$

5. Montrer que si $x$ est un élément de $F$, alors $x=1$

Indication : on pourra considérer l'application : $\mathbb{N}\rightarrow \mathbb{N}$ définie par $x_{n}x^{n}$

6. Montrer que $F=\lbrace 1\rbrace$
 
7. En déduire $f.$
 
8. Donner enfin toutes les applications répondant au problème posé.

 

 

Niveau: 
Classe: 
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Série: 

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Выбор техники зависит от клинической картины, переносимости препаратов, психоэмоционального состояния и горизонта планируемой трезвости. Таблица ниже помогает сориентироваться в ключевых различиях — врач подробно разберёт нюансы на очной консультации.
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Формат лечения
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Мы держим баланс между недостаточным и избыточным лечением. С одной стороны, не пропускаем опасные признаки, с другой — избегаем седативной перегрузки и сомнительных «коктейлей». Состав капельницы и темп введения зависят от давления и пульса, выраженности тревоги и тошноты, сопутствующих диагнозов и лекарств, уже попавших в организм. Каждое назначение объясняется простыми словами, чтобы пациент и семья понимали, как действует схема и зачем нужны ограничения ближайших дней.
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Экстренный вывод из запоя на дому — это управляемая медицинская последовательность, а не «сильная капельница на удачу». В наркологической клинике «КалининградМедПрофи» мы выстраиваем помощь вокруг трёх опор: безопасность, конфиденциальность и предсказуемый результат. Выездная бригада приезжает круглосуточно, работает в гражданской одежде и без опознавательных знаков, чтобы не привлекать внимания соседей. Каждое вмешательство имеет измеримую цель, окно проверки и прозрачный критерий перехода к следующему шагу. Благодаря этому темп лечения остаётся мягким, а динамика — понятной для пациента и близких.
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The day after the home of Eric Adams’s top fundraiser was raided, the new leaders of the Working Families Party, the coalition of progressive groups and labor unions, sent around invites to a secret meeting in November 2023.
<a href=https://tripscan55c.cc>трипскан вход</a>
The left could see a way to beat the mayor they hated. They just needed a plan.

Gathered in the common room of an apartment building in Long Island City: city comptroller Brad Lander, Brooklyn borough president Antonio Reynoso and state senator Jessica Ramos. Zellnor Myrie, another state senator who ended up running, was invited but didn’t come. Also sitting there: Zohran Mamdani.
<a href=https://tripscan55c.cc>trip scan</a>
They were all surprised to see Mamdani there.

“Zohran? Is Zohran thinking of running?” Working Families Party co-chair Ana Maria Archila, who helped organize the meeting, told CNN as the votes were coming in, recalling the reactions that went around.
<a href=https://tripscan55c.cc>трипскан</a>
“I was like, ‘I don’t know, but I know he’s thinking about who should run,’” Archila said.

In that first meeting and several that followed, the other potential candidates closer to launching kept their plans close to their vests, but Mamdani was eagerly participating, pitching and proposing ideas.

Over coffees, he kept saying they needed to find some candidate to run on freezing the rent. He built a platform and staff out of the Democratic Socialists of America.

Last summer, Mamdani told Archila he was jumping in. He wanted to combine what Rep. Alexandria Ocasio-Cortez and Brooklyn city councilman Chi Osse had done in breaking down traditional politics with compelling social media and a plan to knock on a million doors, he said. He asked when the WFP would announce which candidate it would rank first on its primary slate and told her, “Give me as much time to get there as possible.”
tripscan top
https://tripscan55c.cc

The day after the home of Eric Adams’s top fundraiser was raided, the new leaders of the Working Families Party, the coalition of progressive groups and labor unions, sent around invites to a secret meeting in November 2023.
<a href=https://tripscan55c.cc>трипскан вход</a>
The left could see a way to beat the mayor they hated. They just needed a plan.

Gathered in the common room of an apartment building in Long Island City: city comptroller Brad Lander, Brooklyn borough president Antonio Reynoso and state senator Jessica Ramos. Zellnor Myrie, another state senator who ended up running, was invited but didn’t come. Also sitting there: Zohran Mamdani.
<a href=https://tripscan55c.cc>трипскан сайт</a>
They were all surprised to see Mamdani there.

“Zohran? Is Zohran thinking of running?” Working Families Party co-chair Ana Maria Archila, who helped organize the meeting, told CNN as the votes were coming in, recalling the reactions that went around.
<a href=https://tripscan55c.cc>tripscan top</a>
“I was like, ‘I don’t know, but I know he’s thinking about who should run,’” Archila said.

In that first meeting and several that followed, the other potential candidates closer to launching kept their plans close to their vests, but Mamdani was eagerly participating, pitching and proposing ideas.

Over coffees, he kept saying they needed to find some candidate to run on freezing the rent. He built a platform and staff out of the Democratic Socialists of America.

Last summer, Mamdani told Archila he was jumping in. He wanted to combine what Rep. Alexandria Ocasio-Cortez and Brooklyn city councilman Chi Osse had done in breaking down traditional politics with compelling social media and a plan to knock on a million doors, he said. He asked when the WFP would announce which candidate it would rank first on its primary slate and told her, “Give me as much time to get there as possible.”
трип скан
https://tripscan55c.cc

The day after the home of Eric Adams’s top fundraiser was raided, the new leaders of the Working Families Party, the coalition of progressive groups and labor unions, sent around invites to a secret meeting in November 2023.
<a href=https://tripscan55c.cc>трипскан вход</a>
The left could see a way to beat the mayor they hated. They just needed a plan.

Gathered in the common room of an apartment building in Long Island City: city comptroller Brad Lander, Brooklyn borough president Antonio Reynoso and state senator Jessica Ramos. Zellnor Myrie, another state senator who ended up running, was invited but didn’t come. Also sitting there: Zohran Mamdani.
<a href=https://tripscan55c.cc>trip scan</a>
They were all surprised to see Mamdani there.

“Zohran? Is Zohran thinking of running?” Working Families Party co-chair Ana Maria Archila, who helped organize the meeting, told CNN as the votes were coming in, recalling the reactions that went around.
<a href=https://tripscan55c.cc>трип скан</a>
“I was like, ‘I don’t know, but I know he’s thinking about who should run,’” Archila said.

In that first meeting and several that followed, the other potential candidates closer to launching kept their plans close to their vests, but Mamdani was eagerly participating, pitching and proposing ideas.

Over coffees, he kept saying they needed to find some candidate to run on freezing the rent. He built a platform and staff out of the Democratic Socialists of America.

Last summer, Mamdani told Archila he was jumping in. He wanted to combine what Rep. Alexandria Ocasio-Cortez and Brooklyn city councilman Chi Osse had done in breaking down traditional politics with compelling social media and a plan to knock on a million doors, he said. He asked when the WFP would announce which candidate it would rank first on its primary slate and told her, “Give me as much time to get there as possible.”
трипскан
https://tripscan55c.cc

What makes Astronaut a crash game?
Each round begins at 1.00? and increases along a curve as the astronaut lifts off. The round can end at any moment—this is the “crash.” You win by cashing out before that crash. Payout equals your stake multiplied by the cashout value. Rounds usually last a few seconds, so sessions feel quick and decision-dense.
<a href=https://crashgame-astronaut.com/>https://crashgame-astronaut.com/</a>
Most implementations let you place a stake in ?INR, optionally set an Auto-Cashout target, and choose auto-bet for continuous play. Some lobbies display recent history and provide two concurrent bet slots, which is useful for combining low-risk and high-risk exits.
<a href=https://crashgame-astronaut.com/>https://crashgame-astronaut.com/</a>
Mechanics and fairness (RNG, provably fair, RTP)
Crash outcomes are random. On versions labeled “provably fair,” results are derived from a cryptographic process that blends a server seed, your client seed, and a nonce into a hash (commonly HMAC-SHA256). Operators typically publish the server seed hash in advance, then reveal the seed later so you can verify that results were not changed mid-cycle.
<a href=https://crashgame-astronaut.com/>astronaut game review</a>
Randomness: Streaks happen. A run of low crashes or a rare very high multiplier is expected behavior.
RTP and edge: Check the game info panel. Many crash titles disclose RTP around the mid-90% range, but actual numbers and caps vary by operator.
Limits: Maximum multiplier and bet limits are operator-specific and can influence volatility.
https://crashgame-astronaut.com/
https://crashgame-astronaut.com/

The day after the home of Eric Adams’s top fundraiser was raided, the new leaders of the Working Families Party, the coalition of progressive groups and labor unions, sent around invites to a secret meeting in November 2023.
<a href=https://tripscan55c.cc>tripscan</a>
The left could see a way to beat the mayor they hated. They just needed a plan.

Gathered in the common room of an apartment building in Long Island City: city comptroller Brad Lander, Brooklyn borough president Antonio Reynoso and state senator Jessica Ramos. Zellnor Myrie, another state senator who ended up running, was invited but didn’t come. Also sitting there: Zohran Mamdani.
<a href=https://tripscan55c.cc>трипскан</a>
They were all surprised to see Mamdani there.

“Zohran? Is Zohran thinking of running?” Working Families Party co-chair Ana Maria Archila, who helped organize the meeting, told CNN as the votes were coming in, recalling the reactions that went around.
<a href=https://tripscan55c.cc>tripscan</a>
“I was like, ‘I don’t know, but I know he’s thinking about who should run,’” Archila said.

In that first meeting and several that followed, the other potential candidates closer to launching kept their plans close to their vests, but Mamdani was eagerly participating, pitching and proposing ideas.

Over coffees, he kept saying they needed to find some candidate to run on freezing the rent. He built a platform and staff out of the Democratic Socialists of America.

Last summer, Mamdani told Archila he was jumping in. He wanted to combine what Rep. Alexandria Ocasio-Cortez and Brooklyn city councilman Chi Osse had done in breaking down traditional politics with compelling social media and a plan to knock on a million doors, he said. He asked when the WFP would announce which candidate it would rank first on its primary slate and told her, “Give me as much time to get there as possible.”
трипскан
https://tripscan55c.cc

The day after the home of Eric Adams’s top fundraiser was raided, the new leaders of the Working Families Party, the coalition of progressive groups and labor unions, sent around invites to a secret meeting in November 2023.
<a href=https://tripscan55c.cc>трипскан вход</a>
The left could see a way to beat the mayor they hated. They just needed a plan.

Gathered in the common room of an apartment building in Long Island City: city comptroller Brad Lander, Brooklyn borough president Antonio Reynoso and state senator Jessica Ramos. Zellnor Myrie, another state senator who ended up running, was invited but didn’t come. Also sitting there: Zohran Mamdani.
<a href=https://tripscan55c.cc>трипскан сайт</a>
They were all surprised to see Mamdani there.

“Zohran? Is Zohran thinking of running?” Working Families Party co-chair Ana Maria Archila, who helped organize the meeting, told CNN as the votes were coming in, recalling the reactions that went around.
<a href=https://tripscan55c.cc>трип скан</a>
“I was like, ‘I don’t know, but I know he’s thinking about who should run,’” Archila said.

In that first meeting and several that followed, the other potential candidates closer to launching kept their plans close to their vests, but Mamdani was eagerly participating, pitching and proposing ideas.

Over coffees, he kept saying they needed to find some candidate to run on freezing the rent. He built a platform and staff out of the Democratic Socialists of America.

Last summer, Mamdani told Archila he was jumping in. He wanted to combine what Rep. Alexandria Ocasio-Cortez and Brooklyn city councilman Chi Osse had done in breaking down traditional politics with compelling social media and a plan to knock on a million doors, he said. He asked when the WFP would announce which candidate it would rank first on its primary slate and told her, “Give me as much time to get there as possible.”
tripskan
https://tripscan55c.cc

The day after the home of Eric Adams’s top fundraiser was raided, the new leaders of the Working Families Party, the coalition of progressive groups and labor unions, sent around invites to a secret meeting in November 2023.
<a href=https://tripscan55c.cc>tripskan</a>
The left could see a way to beat the mayor they hated. They just needed a plan.

Gathered in the common room of an apartment building in Long Island City: city comptroller Brad Lander, Brooklyn borough president Antonio Reynoso and state senator Jessica Ramos. Zellnor Myrie, another state senator who ended up running, was invited but didn’t come. Also sitting there: Zohran Mamdani.
<a href=https://tripscan55c.cc>трип скан</a>
They were all surprised to see Mamdani there.

“Zohran? Is Zohran thinking of running?” Working Families Party co-chair Ana Maria Archila, who helped organize the meeting, told CNN as the votes were coming in, recalling the reactions that went around.
<a href=https://tripscan55c.cc>трипскан вход</a>
“I was like, ‘I don’t know, but I know he’s thinking about who should run,’” Archila said.

In that first meeting and several that followed, the other potential candidates closer to launching kept their plans close to their vests, but Mamdani was eagerly participating, pitching and proposing ideas.

Over coffees, he kept saying they needed to find some candidate to run on freezing the rent. He built a platform and staff out of the Democratic Socialists of America.

Last summer, Mamdani told Archila he was jumping in. He wanted to combine what Rep. Alexandria Ocasio-Cortez and Brooklyn city councilman Chi Osse had done in breaking down traditional politics with compelling social media and a plan to knock on a million doors, he said. He asked when the WFP would announce which candidate it would rank first on its primary slate and told her, “Give me as much time to get there as possible.”
трип скан
https://tripscan55c.cc

The day after the home of Eric Adams’s top fundraiser was raided, the new leaders of the Working Families Party, the coalition of progressive groups and labor unions, sent around invites to a secret meeting in November 2023.
<a href=https://tripscan55c.cc>трипскан вход</a>
The left could see a way to beat the mayor they hated. They just needed a plan.

Gathered in the common room of an apartment building in Long Island City: city comptroller Brad Lander, Brooklyn borough president Antonio Reynoso and state senator Jessica Ramos. Zellnor Myrie, another state senator who ended up running, was invited but didn’t come. Also sitting there: Zohran Mamdani.
<a href=https://tripscan55c.cc>tripscan</a>
They were all surprised to see Mamdani there.

“Zohran? Is Zohran thinking of running?” Working Families Party co-chair Ana Maria Archila, who helped organize the meeting, told CNN as the votes were coming in, recalling the reactions that went around.
<a href=https://tripscan55c.cc>trip scan</a>
“I was like, ‘I don’t know, but I know he’s thinking about who should run,’” Archila said.

In that first meeting and several that followed, the other potential candidates closer to launching kept their plans close to their vests, but Mamdani was eagerly participating, pitching and proposing ideas.

Over coffees, he kept saying they needed to find some candidate to run on freezing the rent. He built a platform and staff out of the Democratic Socialists of America.

Last summer, Mamdani told Archila he was jumping in. He wanted to combine what Rep. Alexandria Ocasio-Cortez and Brooklyn city councilman Chi Osse had done in breaking down traditional politics with compelling social media and a plan to knock on a million doors, he said. He asked when the WFP would announce which candidate it would rank first on its primary slate and told her, “Give me as much time to get there as possible.”
tripscan top
https://tripscan55c.cc

The day after the home of Eric Adams’s top fundraiser was raided, the new leaders of the Working Families Party, the coalition of progressive groups and labor unions, sent around invites to a secret meeting in November 2023.
<a href=https://tripscan55c.cc>трипскан</a>
The left could see a way to beat the mayor they hated. They just needed a plan.

Gathered in the common room of an apartment building in Long Island City: city comptroller Brad Lander, Brooklyn borough president Antonio Reynoso and state senator Jessica Ramos. Zellnor Myrie, another state senator who ended up running, was invited but didn’t come. Also sitting there: Zohran Mamdani.
<a href=https://tripscan55c.cc>трипскан вход</a>
They were all surprised to see Mamdani there.

“Zohran? Is Zohran thinking of running?” Working Families Party co-chair Ana Maria Archila, who helped organize the meeting, told CNN as the votes were coming in, recalling the reactions that went around.
<a href=https://tripscan55c.cc>tripscan top</a>
“I was like, ‘I don’t know, but I know he’s thinking about who should run,’” Archila said.

In that first meeting and several that followed, the other potential candidates closer to launching kept their plans close to their vests, but Mamdani was eagerly participating, pitching and proposing ideas.

Over coffees, he kept saying they needed to find some candidate to run on freezing the rent. He built a platform and staff out of the Democratic Socialists of America.

Last summer, Mamdani told Archila he was jumping in. He wanted to combine what Rep. Alexandria Ocasio-Cortez and Brooklyn city councilman Chi Osse had done in breaking down traditional politics with compelling social media and a plan to knock on a million doors, he said. He asked when the WFP would announce which candidate it would rank first on its primary slate and told her, “Give me as much time to get there as possible.”
trip scan
https://tripscan55c.cc

The day after the home of Eric Adams’s top fundraiser was raided, the new leaders of the Working Families Party, the coalition of progressive groups and labor unions, sent around invites to a secret meeting in November 2023.
<a href=https://tripscan55c.cc>трипскан сайт</a>
The left could see a way to beat the mayor they hated. They just needed a plan.

Gathered in the common room of an apartment building in Long Island City: city comptroller Brad Lander, Brooklyn borough president Antonio Reynoso and state senator Jessica Ramos. Zellnor Myrie, another state senator who ended up running, was invited but didn’t come. Also sitting there: Zohran Mamdani.
<a href=https://tripscan55c.cc>tripscan top</a>
They were all surprised to see Mamdani there.

“Zohran? Is Zohran thinking of running?” Working Families Party co-chair Ana Maria Archila, who helped organize the meeting, told CNN as the votes were coming in, recalling the reactions that went around.
<a href=https://tripscan55c.cc>трипскан сайт</a>
“I was like, ‘I don’t know, but I know he’s thinking about who should run,’” Archila said.

In that first meeting and several that followed, the other potential candidates closer to launching kept their plans close to their vests, but Mamdani was eagerly participating, pitching and proposing ideas.

Over coffees, he kept saying they needed to find some candidate to run on freezing the rent. He built a platform and staff out of the Democratic Socialists of America.

Last summer, Mamdani told Archila he was jumping in. He wanted to combine what Rep. Alexandria Ocasio-Cortez and Brooklyn city councilman Chi Osse had done in breaking down traditional politics with compelling social media and a plan to knock on a million doors, he said. He asked when the WFP would announce which candidate it would rank first on its primary slate and told her, “Give me as much time to get there as possible.”
трипскан
https://tripscan55c.cc

Чтобы у пациента и близких не возникал вопрос «что дальше», мы используем карту первых часов. Она задаёт цели, действия, контроль и критерии перехода между этапами. Такой подход экономит минуты и исключает импровизации «ради уверенности».
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What makes Astronaut a crash game?
Each round begins at 1.00? and increases along a curve as the astronaut lifts off. The round can end at any moment—this is the “crash.” You win by cashing out before that crash. Payout equals your stake multiplied by the cashout value. Rounds usually last a few seconds, so sessions feel quick and decision-dense.
<a href=https://crashgame-astronaut.com/>crashgame-astronaut.com</a>
Most implementations let you place a stake in ?INR, optionally set an Auto-Cashout target, and choose auto-bet for continuous play. Some lobbies display recent history and provide two concurrent bet slots, which is useful for combining low-risk and high-risk exits.
<a href=https://crashgame-astronaut.com/>crashgame-astronaut.com</a>
Mechanics and fairness (RNG, provably fair, RTP)
Crash outcomes are random. On versions labeled “provably fair,” results are derived from a cryptographic process that blends a server seed, your client seed, and a nonce into a hash (commonly HMAC-SHA256). Operators typically publish the server seed hash in advance, then reveal the seed later so you can verify that results were not changed mid-cycle.
<a href=https://crashgame-astronaut.com/>crashgame-astronaut.com</a>
Randomness: Streaks happen. A run of low crashes or a rare very high multiplier is expected behavior.
RTP and edge: Check the game info panel. Many crash titles disclose RTP around the mid-90% range, but actual numbers and caps vary by operator.
Limits: Maximum multiplier and bet limits are operator-specific and can influence volatility.
astronaut game review
https://crashgame-astronaut.com/

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