The sky is being coloured more azure as we continue our journey.

"Behold, the Twilight Zone! Before this site became a really well-known tourist attraction, this area was a tropical rainforest. But this place was unearthed landing on our planet on 21 September 1977, not so long after the Voyagers were launched by the National Aeronautics and Space Administration.

The land steadily expanded for the next few years until it was quadruple in size.

And then the most destructive storm in the history of my homeland happened in 1993 that killed and injured millions of people. The hurricane also destroyed vehicles, buildings, bridges, overpasses and roadways,... and resulted in economic damage. (And the government still reinvested money in building the railway which is not worth all of the endurance the locomotives had to go through.)

The storm tore the whole forest free from the shore. And it became a landlocked island. The tropical rainforest looked unharmed after the incident."

"You meant a tussock?"

"Yes, a tussock. After that, a railway was built over the tussock for tourists to visit there."

"Seriously? A natural occurrence of tussocks is that they continually move around on wetland locations."

"Correct. That's why the train tracks didn't last long. At least, they collected all of the material on and beneath the tussock. Because of that, the forest looks untouched. The lake isn't polluted and exceptionally rich in aquatic lifeforms."

"You can give back my smartphone now. It is almost out-of-battery."

"What I am holding here is a phone, not a firearm before the action has returned to the normal firing position. Use English accurately."

"Okay, fine, I will. My smartphone needs to be recharged. Now give it back to me!"

"Here you go."

"Thanks, I've got my backup charger. Please do not use my phone without my permission again, won't you?"

"Sorry for taking your phone away."

"Don't worry, it's not that serious. But how are we going to get there?"

"Portals. At the night when the storm happened, cloud-to-ground lightning tore the sky, and the land, and the water and created portals that are invisible to human perception. But they portals always work, just jump into the water.

Believe it or not, on the floor of the lake, there is another portal that leads to the tussock's home planet before it flew to Earth. It was scientifically proven in 2010. And no one has ever gone through that portal. You have to sacrifice your life just to go through an unexplained passage to another world. Who knows if you'll ever come back home? And if you'll manage to do so, who knows if you'll come back alive?"

"I would do that. That sounds fun. Wait, are you looking for information on my smartphone again?"

"There is a sign over there that says it all. Also, motormen learn this, it is not needed, but it's fun learning about the history of rail transport."

"When the world couldn't get any weirder, we have this."

"The train stops here. When the tourists enter the tropical rainforest, the locomotive automatically transports to a station on the other side of the lake. Now jump to the water."

...

"Here we are! Enter the Twilight Zone! At here, you won't be alone anymore. That is what the attendants said before one of them disappeared."

"What happened?"

"We don't know. Anyway, there is an abandoned restaurant here. Care to join me?"

"You know all of that and people said that you have Alzheimer's."

"Remember, there is always a sign that says it all."

We arrive at the eatery. Although it looks overgrown on the outside, it is actually clean in the inside. There were no leftovers from centuries ago. Looks like the government really care about the environment of this particular place.

"This restaurant might look healthful, but that doesn't mean you should put your cinnamon rolls on the silverware here."

"I have that in my school bag. They are made fresh daily from scratch in a bakery near my house. Would you like them?"

"Definitely. We haven't eaten anything since yesterday. I am starving. Thanks!"

"It is now twenty-one minutes past eleven, or 11:21. Let me see if could write 1121 using 12 copies of 12 and the operations: adding and subtracting, multiplying and dividing."

A few minutes later he says - "This is not possible." and then explains it to me for the next twenty minutes.

"How did you do that so quickly and correctly to every word you spoke?"

"I don't know. It was an instinct."

"Well, people told me that you were the most intelligent student in school, especially at three-dimensional geometry. It didn't come as a surprise as the school you studied was only a couple footsteps away from your home. You came to school early in the morning and came home late at night. It has become a practice of yours. You didn't seem to out-work yourself.

There was not a day you didn't go to school. There was not a walk to the principle's office because of your heedlessness or your carelessness. Perhaps you were the student teachers wanted to be acknowledged in their class."

"I... didn't remember my childhood at all."

"Your life was more interesting than most of us are. Trust me. Also, 1121 is the smallest positive integer to have this property."

"What would you like for brunch?" - A mysterious voice comes from the counter.

"Well, I will check if there are any humanoids at the counter."

"I will go with you. We need to be together." There was no one there.

To be continued. I know that posting literature on a website based around math and science is not worth it. But it is worth a try.

All of the events in the story are fictional, except the launch of the Voyagers.

Try to write 1121 using 12 copies of 12, the operations: adding and subtracting, multiplying and dividing and brackets.

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## Comments

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TopNewestMy first try\( 1121 = 12^3 - 607 \)

but 607 is very difficult to get.

Second try\( 1121 = 12^2 \cdot 8 - 31 \)

\( 8 = 12 \cdot \frac {12+12}{12+12+12} \)

\( 31 = \frac {12}{12+12} \cdot (12+12+12+12+12) + \frac {12}{12} \)

It works, but takes 19 12's.

Third try\( 1121 = 19 \cdot 59 \)

\( 19 = 12 \cdot \frac {12+12+12}{12+12} + \frac {12}{12} \)

\( 59 = 12+12+12+12+12-\frac {12}{12} \)

This takes 15 12's.

\( 59 = 12 \cdot (12 \cdot \frac {12}{12+12}-\frac {12}{12}) - \frac {12}{12} \)

is a little bit worse with 17 12's.

Fourth try\( 1121 = 11 \cdot 103 - 12 \)

\( 11 = 12 - \frac {12}{12} \)

\( 103 = \left( 12 \cdot \frac {12+12+12}{12+12} \right) + 12 + \frac {12}{12+12} + \frac {12}{12} \)

16.

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The truth is, it is still impossible, even with brackets.

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How did you prove this?

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this website.

I don't know. I got it fromLog in to reply

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using 13 12's.

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This works!

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It might still be impossible.

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