Olympiades ENSAE - 1er S 2025
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.
Commentaires
DavidAnato (non vérifié)
sam, 10/04/2025 - 15:13
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Disney made a smart choice’
Despite the comparisons, Abu Dhabi isn’t positioning itself as a direct rival to Orlando — it’s aiming to be something more. The emirate sees its theme parks as part of a bigger portfolio of attractions, alongside cultural landmarks, luxury hotels, pristine beaches, and desert adventures.
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A 15-minute drive from Yas Island, Saadiyat Island is home to the Louvre Abu Dhabi, a franchised outpost of the famous Paris art museum, which welcomed 1.4 million visitors last year, 84% from abroad. The Guggenheim Abu Dhabi and Zayed National Museum are both under construction, adding to a cultural district that will be one of the region’s most concentrated hubs of art and heritage.
“Abu Dhabi’s unique appeal lies in the diversity of our tourism offering,” Al Geziry added. “For thrill-seekers, we have record-breaking roller coasters and dune bashing in the desert. For culture lovers, historic sites like Al Ain Oasis and institutions like the Saadiyat museums. And for luxury travelers, world-class dining, private island resorts, and high-end shopping.
“Where else can you start your day under the Louvre’s iconic rain-of-light dome and end it in the immersive, story-driven worlds of Warner Bros. World or Ferrari World?”
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Still, not everyone is convinced that Disney’s expansion into the Middle East is a sure bet.
“The region has seen its share of false starts,” says Dennis Speigel, founder of the International Theme Park Services consultancy, comparing it to neighboring Dubai’s patchy record with theme park expansion ambitions in the mid-2010s. “Several of them struggled for profitability in their first decade.”
Related article
Saadiyat Cultural District in Abu Dhabi is set to become one of the world’s preeminent arts and culture hubs, with one of the highest concentrations of cultural institutions globally. But the area isn’t just for art connoisseurs. Explore what to do in the new district, from iconic museums to luxurious beach days to decadent dining options.
You can walk between the Louvre and the Guggenheim in this new art district
Spiegel believes Abu Dhabi is different. “Disney made a smart choice. The infrastructure, safety, and existing leisure developments create an ideal entry point,” he told CNN earlier this year. “It’s a much more controlled and calculated move.”
Under its Tourism Strategy 2030, Abu Dhabi aims to grow annual visitors from 24 million in 2023 to more than 39 million by the end of the decade. With Disneyland as a centerpiece, those targets may well be surpassed. The city’s population has already grown from 2.7 million in 2014 to more than 4.1 million today, a reflection of its rising profile as a regional hub.
Yas Island alone has been transformed in the space of a decade from a largely undeveloped stretch of sand to a self-contained resort destination, complete with golf courses, marinas, a mall, more than 160 restaurants, and a cluster of high-end hotels.
Orlando’s head start remains formidable — it still offers multiple Disney and Universal parks, has decades of brand loyalty, and an infrastructure built to handle tens of millions of tourists annually.
But Abu Dhabi is catching up fast. Its combination of frictionless travel, year-round comfort, cutting-edge attractions, and a cultural scene that adds depth to the experience gives Abu Dhabi its own unique selling point, potentially offering a model for the next generation of theme park capital.
Anya138sn (non vérifié)
sam, 10/04/2025 - 15:16
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From beaches to golf courses: The world’s most unusual airport runways
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When it comes to travel, wherever you are in the world, some things never change. McDonald’s is always McDonald’s. A hotel lobby is always a hotel lobby. An inflight safety demonstration is always a safety demonstration, and an airport runway is an airport runway: a long, clean-lined strip of asphalt free of all external interference; a sterile environment that could be anywhere on the planet.
Or maybe not. Because when it comes to airport runways, once the safety side is taken care of, in a few parts of the world, things get a little inventive. Maybe you’ll land on a manmade island in the middle of the sea. Maybe you’ll wave at golfers on the 18-hole course between the two runways. Or maybe you’ll hit the beach faster than expected — by stepping off the airplane onto the sand.
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From runways you can drive across to weird and wonderful airport locations, here are 12 of our favorite out-there runways.
Barra Airport, Scotland (BRR)
If nothing comes between you and your beach break, then Barra, in Scotland’s Outer Hebrides, is your kind of airport. This is the only place in the world where the runway is on the beach itself.
Just one flight route operates here: Loganair’s 140-mile connection with Glasgow, using 19-seater de Havilland Canada DHC-6 Twin Otter aircraft. Pilots heading to Barra — an island just eight miles long — must line up and touch down on Traigh Mhor, a wide bay in the north of the island (if Barra is shaped like a turtle, Traigh Mhor is its neck), landing straight onto the sand. Flights must be timed with the tides to allow as much space to land and take off as possible.
Passengers walk across the beach to the terminal on the other side of the dunes, then get a last bit of sand underfoot as they board the aircraft for the flight back to the mainland. With these conditions, it’s little wonder that flights are canceled with a fair amount of regularity — so you may want to build in extra time before planning onward connections.
But even a delayed return is worth it for avgeeks. On this tiny plane, passengers experience the flight in close proximity to the pilots — when CNN took a spin on the flight in 2019, they could even see the pilot’s GPS instruments from their seat.
Related article
A lead photo of various travel products that can help pass time in airports
CNN Underscored: Flight delayed? These 14 products will help you pass the time at the airport
Hong Kong International Airport (HKG)
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport.
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport. d3sign/Moment RF/Getty Images
For the busiest cargo airport in the world, you need space. Luckily, Hong Kong created an entire island for its airport which, when it opened, had the world’s largest passenger terminal, too. Built to replace its predecessor (a single runway in crowded Kowloon, which was notorious for its violent turns on take-off and landing), HKG sits over the original islet of Chek Lap Kok, which was quadrupled in size with reclaimed land to house the two-runway airport. President Bill Clinton was among the first foreigners to touch down after the airport opened in 1998.
Located next to Lantau Island, the airport has views for days — the sides of the terminals are largely glass, built to shatter (and therefore preserve the building) during potential typhoons. Even getting there is a treat — the 1.4-mile Tsing Ma bridge, which connects HKG to Ma Wan island, heading towards the city, debuted as the longest road-and-rail suspension bridge in the world.
EmorybAp (non vérifié)
sam, 10/04/2025 - 16:05
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tripskan
From beaches to golf courses: The world’s most unusual airport runways
<a href=http://trips45.cc>трип скан</a>
When it comes to travel, wherever you are in the world, some things never change. McDonald’s is always McDonald’s. A hotel lobby is always a hotel lobby. An inflight safety demonstration is always a safety demonstration, and an airport runway is an airport runway: a long, clean-lined strip of asphalt free of all external interference; a sterile environment that could be anywhere on the planet.
Or maybe not. Because when it comes to airport runways, once the safety side is taken care of, in a few parts of the world, things get a little inventive. Maybe you’ll land on a manmade island in the middle of the sea. Maybe you’ll wave at golfers on the 18-hole course between the two runways. Or maybe you’ll hit the beach faster than expected — by stepping off the airplane onto the sand.
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tripskan
From runways you can drive across to weird and wonderful airport locations, here are 12 of our favorite out-there runways.
Barra Airport, Scotland (BRR)
If nothing comes between you and your beach break, then Barra, in Scotland’s Outer Hebrides, is your kind of airport. This is the only place in the world where the runway is on the beach itself.
Just one flight route operates here: Loganair’s 140-mile connection with Glasgow, using 19-seater de Havilland Canada DHC-6 Twin Otter aircraft. Pilots heading to Barra — an island just eight miles long — must line up and touch down on Traigh Mhor, a wide bay in the north of the island (if Barra is shaped like a turtle, Traigh Mhor is its neck), landing straight onto the sand. Flights must be timed with the tides to allow as much space to land and take off as possible.
Passengers walk across the beach to the terminal on the other side of the dunes, then get a last bit of sand underfoot as they board the aircraft for the flight back to the mainland. With these conditions, it’s little wonder that flights are canceled with a fair amount of regularity — so you may want to build in extra time before planning onward connections.
But even a delayed return is worth it for avgeeks. On this tiny plane, passengers experience the flight in close proximity to the pilots — when CNN took a spin on the flight in 2019, they could even see the pilot’s GPS instruments from their seat.
Related article
A lead photo of various travel products that can help pass time in airports
CNN Underscored: Flight delayed? These 14 products will help you pass the time at the airport
Hong Kong International Airport (HKG)
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport.
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport. d3sign/Moment RF/Getty Images
For the busiest cargo airport in the world, you need space. Luckily, Hong Kong created an entire island for its airport which, when it opened, had the world’s largest passenger terminal, too. Built to replace its predecessor (a single runway in crowded Kowloon, which was notorious for its violent turns on take-off and landing), HKG sits over the original islet of Chek Lap Kok, which was quadrupled in size with reclaimed land to house the two-runway airport. President Bill Clinton was among the first foreigners to touch down after the airport opened in 1998.
Located next to Lantau Island, the airport has views for days — the sides of the terminals are largely glass, built to shatter (and therefore preserve the building) during potential typhoons. Even getting there is a treat — the 1.4-mile Tsing Ma bridge, which connects HKG to Ma Wan island, heading towards the city, debuted as the longest road-and-rail suspension bridge in the world.
RamonKen (non vérifié)
sam, 10/04/2025 - 16:06
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From beaches to golf courses: The world’s most unusual airport runways
<a href=http://trips45.cc>tripscan</a>
When it comes to travel, wherever you are in the world, some things never change. McDonald’s is always McDonald’s. A hotel lobby is always a hotel lobby. An inflight safety demonstration is always a safety demonstration, and an airport runway is an airport runway: a long, clean-lined strip of asphalt free of all external interference; a sterile environment that could be anywhere on the planet.
Or maybe not. Because when it comes to airport runways, once the safety side is taken care of, in a few parts of the world, things get a little inventive. Maybe you’ll land on a manmade island in the middle of the sea. Maybe you’ll wave at golfers on the 18-hole course between the two runways. Or maybe you’ll hit the beach faster than expected — by stepping off the airplane onto the sand.
http://trips45.cc
tripscan top
From runways you can drive across to weird and wonderful airport locations, here are 12 of our favorite out-there runways.
Barra Airport, Scotland (BRR)
If nothing comes between you and your beach break, then Barra, in Scotland’s Outer Hebrides, is your kind of airport. This is the only place in the world where the runway is on the beach itself.
Just one flight route operates here: Loganair’s 140-mile connection with Glasgow, using 19-seater de Havilland Canada DHC-6 Twin Otter aircraft. Pilots heading to Barra — an island just eight miles long — must line up and touch down on Traigh Mhor, a wide bay in the north of the island (if Barra is shaped like a turtle, Traigh Mhor is its neck), landing straight onto the sand. Flights must be timed with the tides to allow as much space to land and take off as possible.
Passengers walk across the beach to the terminal on the other side of the dunes, then get a last bit of sand underfoot as they board the aircraft for the flight back to the mainland. With these conditions, it’s little wonder that flights are canceled with a fair amount of regularity — so you may want to build in extra time before planning onward connections.
But even a delayed return is worth it for avgeeks. On this tiny plane, passengers experience the flight in close proximity to the pilots — when CNN took a spin on the flight in 2019, they could even see the pilot’s GPS instruments from their seat.
Related article
A lead photo of various travel products that can help pass time in airports
CNN Underscored: Flight delayed? These 14 products will help you pass the time at the airport
Hong Kong International Airport (HKG)
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport.
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport. d3sign/Moment RF/Getty Images
For the busiest cargo airport in the world, you need space. Luckily, Hong Kong created an entire island for its airport which, when it opened, had the world’s largest passenger terminal, too. Built to replace its predecessor (a single runway in crowded Kowloon, which was notorious for its violent turns on take-off and landing), HKG sits over the original islet of Chek Lap Kok, which was quadrupled in size with reclaimed land to house the two-runway airport. President Bill Clinton was among the first foreigners to touch down after the airport opened in 1998.
Located next to Lantau Island, the airport has views for days — the sides of the terminals are largely glass, built to shatter (and therefore preserve the building) during potential typhoons. Even getting there is a treat — the 1.4-mile Tsing Ma bridge, which connects HKG to Ma Wan island, heading towards the city, debuted as the longest road-and-rail suspension bridge in the world.
Amandabaink (non vérifié)
sam, 10/04/2025 - 16:19
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JamesKax (non vérifié)
sam, 10/04/2025 - 17:06
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Don Mueang International Airport, Thailand (DMK)
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Are you an avgeek with a mean handicap? Then it’s time to tee off in Bangkok, where Don Mueang International Airport has an 18-hole golf course between its two runways. If you’re nervous from a safety point of view, don’t be — players at the Kantarat course must go through airport-style security before they hit the grass. Oh, you meant safety on the course? Just beware of those flying balls, because there are no barriers between the course and the runways. Players are, at least, shown a red light when a plane is coming in to land so don’t get too distracted by the game.
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Although Suvarnabhumi (BKK) is Bangkok’s main airport these days — it opened in 2006 —Don Mueang, which started out as a Royal Thai Air Force base in 1914, remains Bangkok’s budget airline hub, with brands including Thai Air Asia and Thai Lion Air using it as their base. Although you’re more likely to see narrowbodies these days, you may just get lucky — in 2022, an Emirates A380 made an emergency landing here. Imagine the views from the course that day.
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Sporty airport outfit being worn by writer
CNN Underscored: Flying sucks. Make it better with these comfy airport outfits for women
Sumburgh Airport, Scotland (LSI)
The road south from Lerwick cuts across the runway of Sumburgh Airport on Shetland.
The road south from Lerwick cuts across the runway of Sumburgh Airport on Shetland. Alan Morris/iStock Editorial/Getty Images
Planning a trip to Jarlshof, the extraordinarily well-preserved Bronze Age settlement towards the southern tip of Shetland? You may need to build in some extra time. The ancient and Viking-era ruins, called one of the UK’s greatest archaeological sites, sit just beyond one of the runways of Sumburgh, Shetland’s main airport — and reaching them means driving, cycling or walking across the runway itself.
There’s only one road heading due south from the capital, Lerwick; and while it ducks around most of the airport’s perimeter, skirting the two runways, the road cuts directly across the western end of one of them. A staff member occupies a roadside hut, and before take-offs and landings, comes out to lower a barrier across the road. Once the plane is where it needs to be, up come the barriers and waiting drivers get a friendly thumbs up.
Amata Kabua International Airport, Marshall Islands (MAJ)
Fly into Majuro and you'll skim across the Pacific and land on the runway that's just about as wide as the sandbar-like island itself.
Fly into Majuro and you'll skim across the Pacific and land on the runway that's just about as wide as the sandbar-like island itself. mtcurado/iStockphoto/Getty Images
Imagine flying into Majuro, the capital of the Marshall Islands in Micronesia. You’re descending down, down, and further down towards the Pacific, no land in sight. Then you’re suddenly above a pencil-thin atoll — can you really be about to land here? Yes you are, with cars racing past the runway no less, matching you for speed.
Majuro’s Amata Kabua International Airport gives a whole new meaning to the phrase “water landing”. Its single runway, just shy of 8,000ft, is a slim strip of asphalt over the sandbar that’s barely any wider than the atoll itself — and the island is so remote that when the runway was resurfaced, materials had to be transported from the Philippines, Hong Kong and Korea, according to the constructors. “Lagoon Road” — the 30-mile road that runs from top to toe on Majuro — skims alongside the runway.
Don’t think about pulling over, though — there’s only sand and sea on one side, and that runway the other.
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Barra Airport, Scotland
At Scotland’s beach airport, the runway disappears at high tide
KeithFoums (non vérifié)
sam, 10/04/2025 - 17:40
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Disney made a smart choice’
Despite the comparisons, Abu Dhabi isn’t positioning itself as a direct rival to Orlando — it’s aiming to be something more. The emirate sees its theme parks as part of a bigger portfolio of attractions, alongside cultural landmarks, luxury hotels, pristine beaches, and desert adventures.
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A 15-minute drive from Yas Island, Saadiyat Island is home to the Louvre Abu Dhabi, a franchised outpost of the famous Paris art museum, which welcomed 1.4 million visitors last year, 84% from abroad. The Guggenheim Abu Dhabi and Zayed National Museum are both under construction, adding to a cultural district that will be one of the region’s most concentrated hubs of art and heritage.
“Abu Dhabi’s unique appeal lies in the diversity of our tourism offering,” Al Geziry added. “For thrill-seekers, we have record-breaking roller coasters and dune bashing in the desert. For culture lovers, historic sites like Al Ain Oasis and institutions like the Saadiyat museums. And for luxury travelers, world-class dining, private island resorts, and high-end shopping.
“Where else can you start your day under the Louvre’s iconic rain-of-light dome and end it in the immersive, story-driven worlds of Warner Bros. World or Ferrari World?”
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Still, not everyone is convinced that Disney’s expansion into the Middle East is a sure bet.
“The region has seen its share of false starts,” says Dennis Speigel, founder of the International Theme Park Services consultancy, comparing it to neighboring Dubai’s patchy record with theme park expansion ambitions in the mid-2010s. “Several of them struggled for profitability in their first decade.”
Related article
Saadiyat Cultural District in Abu Dhabi is set to become one of the world’s preeminent arts and culture hubs, with one of the highest concentrations of cultural institutions globally. But the area isn’t just for art connoisseurs. Explore what to do in the new district, from iconic museums to luxurious beach days to decadent dining options.
You can walk between the Louvre and the Guggenheim in this new art district
Spiegel believes Abu Dhabi is different. “Disney made a smart choice. The infrastructure, safety, and existing leisure developments create an ideal entry point,” he told CNN earlier this year. “It’s a much more controlled and calculated move.”
Under its Tourism Strategy 2030, Abu Dhabi aims to grow annual visitors from 24 million in 2023 to more than 39 million by the end of the decade. With Disneyland as a centerpiece, those targets may well be surpassed. The city’s population has already grown from 2.7 million in 2014 to more than 4.1 million today, a reflection of its rising profile as a regional hub.
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But Abu Dhabi is catching up fast. Its combination of frictionless travel, year-round comfort, cutting-edge attractions, and a cultural scene that adds depth to the experience gives Abu Dhabi its own unique selling point, potentially offering a model for the next generation of theme park capital.
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When it comes to travel, wherever you are in the world, some things never change. McDonald’s is always McDonald’s. A hotel lobby is always a hotel lobby. An inflight safety demonstration is always a safety demonstration, and an airport runway is an airport runway: a long, clean-lined strip of asphalt free of all external interference; a sterile environment that could be anywhere on the planet.
Or maybe not. Because when it comes to airport runways, once the safety side is taken care of, in a few parts of the world, things get a little inventive. Maybe you’ll land on a manmade island in the middle of the sea. Maybe you’ll wave at golfers on the 18-hole course between the two runways. Or maybe you’ll hit the beach faster than expected — by stepping off the airplane onto the sand.
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From runways you can drive across to weird and wonderful airport locations, here are 12 of our favorite out-there runways.
Barra Airport, Scotland (BRR)
If nothing comes between you and your beach break, then Barra, in Scotland’s Outer Hebrides, is your kind of airport. This is the only place in the world where the runway is on the beach itself.
Just one flight route operates here: Loganair’s 140-mile connection with Glasgow, using 19-seater de Havilland Canada DHC-6 Twin Otter aircraft. Pilots heading to Barra — an island just eight miles long — must line up and touch down on Traigh Mhor, a wide bay in the north of the island (if Barra is shaped like a turtle, Traigh Mhor is its neck), landing straight onto the sand. Flights must be timed with the tides to allow as much space to land and take off as possible.
Passengers walk across the beach to the terminal on the other side of the dunes, then get a last bit of sand underfoot as they board the aircraft for the flight back to the mainland. With these conditions, it’s little wonder that flights are canceled with a fair amount of regularity — so you may want to build in extra time before planning onward connections.
But even a delayed return is worth it for avgeeks. On this tiny plane, passengers experience the flight in close proximity to the pilots — when CNN took a spin on the flight in 2019, they could even see the pilot’s GPS instruments from their seat.
Related article
A lead photo of various travel products that can help pass time in airports
CNN Underscored: Flight delayed? These 14 products will help you pass the time at the airport
Hong Kong International Airport (HKG)
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport.
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport. d3sign/Moment RF/Getty Images
For the busiest cargo airport in the world, you need space. Luckily, Hong Kong created an entire island for its airport which, when it opened, had the world’s largest passenger terminal, too. Built to replace its predecessor (a single runway in crowded Kowloon, which was notorious for its violent turns on take-off and landing), HKG sits over the original islet of Chek Lap Kok, which was quadrupled in size with reclaimed land to house the two-runway airport. President Bill Clinton was among the first foreigners to touch down after the airport opened in 1998.
Located next to Lantau Island, the airport has views for days — the sides of the terminals are largely glass, built to shatter (and therefore preserve the building) during potential typhoons. Even getting there is a treat — the 1.4-mile Tsing Ma bridge, which connects HKG to Ma Wan island, heading towards the city, debuted as the longest road-and-rail suspension bridge in the world.
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From beaches to golf courses: The world’s most unusual airport runways
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When it comes to travel, wherever you are in the world, some things never change. McDonald’s is always McDonald’s. A hotel lobby is always a hotel lobby. An inflight safety demonstration is always a safety demonstration, and an airport runway is an airport runway: a long, clean-lined strip of asphalt free of all external interference; a sterile environment that could be anywhere on the planet.
Or maybe not. Because when it comes to airport runways, once the safety side is taken care of, in a few parts of the world, things get a little inventive. Maybe you’ll land on a manmade island in the middle of the sea. Maybe you’ll wave at golfers on the 18-hole course between the two runways. Or maybe you’ll hit the beach faster than expected — by stepping off the airplane onto the sand.
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From runways you can drive across to weird and wonderful airport locations, here are 12 of our favorite out-there runways.
Barra Airport, Scotland (BRR)
If nothing comes between you and your beach break, then Barra, in Scotland’s Outer Hebrides, is your kind of airport. This is the only place in the world where the runway is on the beach itself.
Just one flight route operates here: Loganair’s 140-mile connection with Glasgow, using 19-seater de Havilland Canada DHC-6 Twin Otter aircraft. Pilots heading to Barra — an island just eight miles long — must line up and touch down on Traigh Mhor, a wide bay in the north of the island (if Barra is shaped like a turtle, Traigh Mhor is its neck), landing straight onto the sand. Flights must be timed with the tides to allow as much space to land and take off as possible.
Passengers walk across the beach to the terminal on the other side of the dunes, then get a last bit of sand underfoot as they board the aircraft for the flight back to the mainland. With these conditions, it’s little wonder that flights are canceled with a fair amount of regularity — so you may want to build in extra time before planning onward connections.
But even a delayed return is worth it for avgeeks. On this tiny plane, passengers experience the flight in close proximity to the pilots — when CNN took a spin on the flight in 2019, they could even see the pilot’s GPS instruments from their seat.
Related article
A lead photo of various travel products that can help pass time in airports
CNN Underscored: Flight delayed? These 14 products will help you pass the time at the airport
Hong Kong International Airport (HKG)
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport.
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport. d3sign/Moment RF/Getty Images
For the busiest cargo airport in the world, you need space. Luckily, Hong Kong created an entire island for its airport which, when it opened, had the world’s largest passenger terminal, too. Built to replace its predecessor (a single runway in crowded Kowloon, which was notorious for its violent turns on take-off and landing), HKG sits over the original islet of Chek Lap Kok, which was quadrupled in size with reclaimed land to house the two-runway airport. President Bill Clinton was among the first foreigners to touch down after the airport opened in 1998.
Located next to Lantau Island, the airport has views for days — the sides of the terminals are largely glass, built to shatter (and therefore preserve the building) during potential typhoons. Even getting there is a treat — the 1.4-mile Tsing Ma bridge, which connects HKG to Ma Wan island, heading towards the city, debuted as the longest road-and-rail suspension bridge in the world.
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From beaches to golf courses: The world’s most unusual airport runways
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When it comes to travel, wherever you are in the world, some things never change. McDonald’s is always McDonald’s. A hotel lobby is always a hotel lobby. An inflight safety demonstration is always a safety demonstration, and an airport runway is an airport runway: a long, clean-lined strip of asphalt free of all external interference; a sterile environment that could be anywhere on the planet.
Or maybe not. Because when it comes to airport runways, once the safety side is taken care of, in a few parts of the world, things get a little inventive. Maybe you’ll land on a manmade island in the middle of the sea. Maybe you’ll wave at golfers on the 18-hole course between the two runways. Or maybe you’ll hit the beach faster than expected — by stepping off the airplane onto the sand.
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From runways you can drive across to weird and wonderful airport locations, here are 12 of our favorite out-there runways.
Barra Airport, Scotland (BRR)
If nothing comes between you and your beach break, then Barra, in Scotland’s Outer Hebrides, is your kind of airport. This is the only place in the world where the runway is on the beach itself.
Just one flight route operates here: Loganair’s 140-mile connection with Glasgow, using 19-seater de Havilland Canada DHC-6 Twin Otter aircraft. Pilots heading to Barra — an island just eight miles long — must line up and touch down on Traigh Mhor, a wide bay in the north of the island (if Barra is shaped like a turtle, Traigh Mhor is its neck), landing straight onto the sand. Flights must be timed with the tides to allow as much space to land and take off as possible.
Passengers walk across the beach to the terminal on the other side of the dunes, then get a last bit of sand underfoot as they board the aircraft for the flight back to the mainland. With these conditions, it’s little wonder that flights are canceled with a fair amount of regularity — so you may want to build in extra time before planning onward connections.
But even a delayed return is worth it for avgeeks. On this tiny plane, passengers experience the flight in close proximity to the pilots — when CNN took a spin on the flight in 2019, they could even see the pilot’s GPS instruments from their seat.
Related article
A lead photo of various travel products that can help pass time in airports
CNN Underscored: Flight delayed? These 14 products will help you pass the time at the airport
Hong Kong International Airport (HKG)
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport.
In Hong Kong, the islet of Chek Lap Kok was massively extended to create an island big enough to house a major international airport. d3sign/Moment RF/Getty Images
For the busiest cargo airport in the world, you need space. Luckily, Hong Kong created an entire island for its airport which, when it opened, had the world’s largest passenger terminal, too. Built to replace its predecessor (a single runway in crowded Kowloon, which was notorious for its violent turns on take-off and landing), HKG sits over the original islet of Chek Lap Kok, which was quadrupled in size with reclaimed land to house the two-runway airport. President Bill Clinton was among the first foreigners to touch down after the airport opened in 1998.
Located next to Lantau Island, the airport has views for days — the sides of the terminals are largely glass, built to shatter (and therefore preserve the building) during potential typhoons. Even getting there is a treat — the 1.4-mile Tsing Ma bridge, which connects HKG to Ma Wan island, heading towards the city, debuted as the longest road-and-rail suspension bridge in the world.
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The search for a silver lining
The trial of Bryan Kohberger – the man who brutally murdered four University of Idaho students inside their off-campus home – ended in July before it ever truly began when he accepted a plea deal that saw him sentenced to four consecutive life terms in prison without the possibility of an appeal or parole.
Kohberger sat impassively throughout the hearing as the loved ones of each of the four students whose lives he so callously ended repeatedly asked him the same question: Why?
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And when he was finally given the opportunity to answer their questions, he said, “I respectfully decline.”
That decision further fueled the mystery around his motive for murdering Xana Kernodle, Madison Mogen, Ethan Chapin and Kaylee Goncalves.
“There’s no reason for these crimes that could approach anything resembling rationality,” Idaho District Judge Steven Hippler said during Kohberger’s sentencing. “The more we try to extract a reason, the more power and control we give to him.”
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Indeed, academics and former FBI profilers told CNN the challenge of unravelling the criminal mind of a man like Bryan Kohberger is enticing. And while his trial may be over, in many ways, the story of what can be learned from his crimes may have only just begun.
“We want to squeeze any silver lining that we can out of these tragedies,” said Molly Amman, a retired profiler who spent years leading the FBI’s Behavioral Threat Assessment Center.
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Only Kohberger knows
Even seasoned police officers who arrived at 1122 King Road on November 13, 2022, struggled to process the brutality of the crime scene.
All four victims had been ruthlessly stabbed to death before the attacker vanished through the kitchen’s sliding glass door and into the night.
“The female lying on the left half of the bed … was unrecognizable,” one officer would later write of the attack that killed Kaylee Goncalves. “I was unable to comprehend exactly what I was looking at while trying to discern the nature of the injuries.”
Initial interviews with the two surviving housemates gave investigators a loose timeline and a general description of the killer – an athletic, White male who wore a mask that covered most of his face – but little else.
Police later found a Ka-Bar knife sheath next to Madison’s body that would prove to be critical in capturing her killer.
One of the surviving housemates told police about a month before the attacks, Kaylee saw “a dark figure staring at her from the tree line when she took her dog Murphy out to pee.”
“There has been lighthearted talk and jokes made about a stalker in the past,” the officer noted. “All the girls were slightly nervous about it being a fact, though.”
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Kohberger is far from the first killer to deny families and survivors the catharsis that comes with confessing, in detail, to his crimes. But that, former FBI profilers tell CNN, is part of what makes the prospect of studying him infuriating and intriguing.
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