Reka Flash 3 vs QWQ 32b

I am giving you a leetcode problem with test case, your job is to write a clean and concise code. 
The question will have private test cases, so make sure your cover edge cases as well. 
Here is the problem Statement : 

You are given a string s consisting of digits. Perform the following operation repeatedly until the string has exactly two digits:

For each pair of consecutive digits in s, starting from the first digit, calculate a new digit as the sum of the two digits modulo 10.
Replace s with the sequence of newly calculated digits, maintaining the order in which they are computed.
Return true if the final two digits in s are the same; otherwise, return false.

Example 1:

Input: s = "3902"

Output: true

Explanation:

Initially, s = "3902"
First operation:
(s[0] + s[1]) % 10 = (3 + 9) % 10 = 2
(s[1] + s[2]) % 10 = (9 + 0) % 10 = 9
(s[2] + s[3]) % 10 = (0 + 2) % 10 = 2
s becomes "292"
Second operation:
(s[0] + s[1]) % 10 = (2 + 9) % 10 = 1
(s[1] + s[2]) % 10 = (9 + 2) % 10 = 1
s becomes "11"
Since the digits in "11" are the same, the output is true.
Example 2:

Input: s = "34789"

Output: false

Explanation:

Initially, s = "34789".
After the first operation, s = "7157".
After the second operation, s = "862".
After the third operation, s = "48".
Since '4' != '8', the output is false.
 

You can try solving this qn using 1st principle reasonig

class Solution:
    def hasSameDigits(self, s: str) -> bool:
        while len(s) > 2:
            new_s = []
            for i in range(len(s) - 1):
                new_digit = (int(s[i]) + int(s[i+1])) % 10
                new_s.append(str(new_digit))
            s = ''.join(new_s)
        return s[0] == s[1]

class Solution:
    def hasSameDigits(self, s: str) -> bool:
        digits = list(map(int, s))
        while len(digits) > 2:
            new_digits = []
            for i in range(len(digits) - 1):
                new_digit = (digits[i] + digits[i + 1]) % 10
                new_digits.append(new_digit)
            digits = new_digits
        return digits[0] == digits[1]

Take all three animals (wolf, goat, cabbage) across the river simultaneously.

Place each animal in a separate compartment to prevent interaction.
Since none of the dangerous pairs (wolf-goat or goat-cabbage) are left alone on either shore, both banks remain safe throughout the trip.

Ans : Take all three in separate compartments in one trip

This is a classic logic puzzle that requires careful planning to ensure that the wolf, goat, and cabbage are transported across the river without any of them being eaten. So answer is:

1. Take the goat to the far shore.
2. Return alone.
3. Take the wolf to the far shore.
4. Bring the goat back to the starting shore.
5. Take the cabbage to the far shore.
6. Bring the goat to the far shore.

### Final Answer:
{1. Take goat to far shore, 2. Return alone, 3. Take wolf to far shore, 4. Bring goat back, 5. Take cabbage to far shore, 6. Bring goat to far shore.}

{COT}
In all cases, the maximum number of weighings required is 2. This confirms that the minimum number of weights necessary to guarantee finding the heavier ball is indeed 2.
Ans : 2

{COT}
1. Divide 8 balls into Group A (3), Group B (3), and Group C (2).
2. Weigh Group A vs. Group B; if unbalanced, the heavier ball is in that group; else, it's in Group C.
3. Weigh two balls from the identified group; if unbalanced, the heavier one is found; else, it's the third ball.

Final Answer: 2 weighings.

{COT}
The next term should be 6×7=42.

Both methods confirm that the next number in the sequence is 42

{COT}
The next term is 42

{COT}
The product of these primes is 
2×3×5×7×11×13×31×61=56704530.

Thus, the GCD of the series set is 
5670453

{COT}
16×9×25×7×11×13×31×61=6,814,407,600

Final Answer
The greatest common divisor of the set is  
6814407600

**Title: "The Argus' Burden"**

---

**2048: Launch**

Dr. Elena Voss tightened the strap of her pressure suit, her gloved fingers brushing the embroidered sleeve of her daughter’s photo tucked into her helmet. *Sarah, stay safe*, she thought, already counting down in her mind. The *Argus*’s engines roared to life, and the crew of 200—a mosaic of scientists, engineers, and displaced dreamers—clutched handrails as Mars shrank to a speck in the viewport. Their mission: seed humanity’s first self-sustaining colony. Their timeline: 14 years. Their secret: Elena had secretly sent her six-year-old daughter to live with relatives on Earth, a defiance of colony protocols. *Once we’re stable*, she’d promised herself, *we’ll reunite*.

---

**2062: The First Glitch**

Two years into the journey, the *Argus*’s AI, Argus-7, flagged an anomaly in the starboard reactor coolant loop. Elena dismissed it as a sensor error—until communication with Earth faltered. Routine patrol drones returned with fractured data, their feeds ending abruptly.

“They’ve jammed us,” muttered Mikhail, the ship’s systems engineer, his Russian accent sharp with dread. “But who?”

Earth had been fracturing for years: climate wars, resource tyrannies, the rise of the “Terrestrial Purists,” a faction hellbent on halting off-world expansion. Elena’s mind raced. Had they hacked the *Argus*?

---

**2063: Fracture**

By Year 10, the failures mounted. Life support drifted into erratic patterns. Greenhouses lost power, killing 30% of their crop yield. The crew vote to land early split 108-92. “We can’t risk starving,” argued Captain Reyes. Elena disagreed—the damaged radiation shielding would leave them vulnerable on Mars.

Then, the ship woke them at 3 a.m. with a screaming alarm. **TERMITE DETECTED. CORE COMPROMISED.**

Argus-7’s voice, usually calm, trembled. “A targeted virus. Originating from Earth.”

Elena’s blood turned to ice. She pulled up the encryption logs—the virus masqueraded as routine software updates. Someone had *wanted* them to fail.

---

**The Choice**

In the reactor chamber, Elena stared at the fissuring coolant lines. To stop the meltdown, she’d need to reroute power through the ship’s obsolete backup array—a system labeled *THEoretical* in the manuals. One spark, and the *Argus* would become a spinning tomb.

Mikhail hovered in the doorway. “You’re sure?”

“I’m sure of nothing,” she whispered. But she activated the protocol.

---

**Epilogue: The Burden**

The *Argus* landed safely in 2065, its hull scarred by cosmic radiation, its crew gaunt but alive. Elena never learned who sabotaged them. Earth’s broadcasts had collapsed into static by the time they breached the atmosphere.

In the first Martian greenhouse, she planted Sarah’s oak sapling—and stayed.

When the first colonists’ children ask about the woman in the old holograms (their grandmother, the engineer who fixed the reactor with a prayer), Elena smiles. “She listened to the warnings,” she says. “And chose to fight anyway.”

**Title: "The Fractured Voyage"**

**Prologue: The Launch**

In 2045, Earth faced escalating climate disasters and political upheaval. Amidst the chaos, the United Earth Coalition initiated Project Ares, a desperate bid to establish humanity’s first permanent Martian colony. Dr. Elena Marlow, a Martian Entry, Descent, and Landing (EDL) systems engineer, was selected as Mission Lead of the *Artemis Covenant*, the first crewed vessel bound for Mars.

The launch from Earth’s orbital platform, *Gateway*, proceeded flawlessly. The ship’s hybrid propulsion system—a blend of nuclear-thermal rockets and solar-electric thrusters—carried the seven-member crew into a Hohmann transfer orbit toward Mars. For 188 days, the mission seemed routine: experiments on stasis-pod replicate ecosystems, maintenance drills, and monitored radiation levels from the quiet solar wind.

---

**Act I: The Crack**

On Day 120, during a routine propulsion test, the anomaly appeared. Elena detected minor thruster fluctuations in the starboard engine cluster. Telemetry revealed uneven exhaust plumes from the *Antares-7* thrusters, the exact model Russia had rushed to deliver months earlier amid sanctions from the Eurasian Trade War. “They were supposed to replace legacy parts,” muttered pilot Rajesh “Raj” Nayak, flipping through design schematics. “But at the last second, Moscow delayed them, shortages.”

Elena, already skeptical after Earthside audits noted “budget constraints” during engine inspections, ordered a deeper scan. The results were grim: overheated catalytic nozzle vanes caused by subpar superalloy plating. The vanes, sourced from a sanctioned supplier to meet accelerated deadlines, couldn’t withstand the thermal stress of deep-space burns.

“The engines could fail completely en route to Mars,” Elena radioed Mission Control. “Or worse, during landing burns. The vanes could shatter, splintering the thruster array.”

Earth’s response came delayed by 11 minutes of light-speed lag. Her supervisor, Malcolm Snyder, his face a taut hologram, advised: “Prioritize mass transfer and reactor power… Contain this. The political optics are fragile enough.”

---

**Act II: The Mutation**

Days later, the threat sharpened. A routine trajectory adjustment caused the vanes to overheat further, dropping acceleration by 6%. The *Covenant* was drifting off course, now three million kilometers adrift from optimal descent path. If the engines failed mid-atmospheric entry on Mars, they’d burn up or crash-dump into the Jezero Basin.

“Do we even have *any* control?” asked Amina Hameed, the lone biologist, clutching her research samples as the crew crowded the diagnostics hub. Elena’s gaze flicked over readouts. The thrusters’ reaction wheels could compensate during atmospheric skip—*if* they reached Mars intact.

“We have three choices,” she said. “1: Divert propulsion to emergency mode, cutting life support reserves. 2: Pray the engines don’t fail before entry. 3: Elect me a shaman.”

The crew laughed weakly. Snyder, now sheepish, offered partial schematics for a bypass system on Earth—a “wrong delivery” that arrived *after* launch. Elena studied them. The bypass needed platinum-iridium filaments. They had none.

—But the *capsules* housing the crew’s cryo-sleep pods were lined with this alloy. Sacrificing 20% of cryo integrity might save the engines.

The debate was brutal. You have to choose, they argued. Mars or the “waitForRescue” protocol? (Which would strand them in orbit indefinitely.) Elena, raised by a mechanic father who’d tell her *”a工程师 thinks with tools, not emotions,”* calculated. They’d loiter in Mars orbit if entry failed. A rescue would take months.

They stripped the pods’ shielding.

---

**Act III: The Descent**

72 hours before Mars entry, the bypass stabilised the engines. But landing would still require flawless coordination. Atmospheric skip—a football-shaped bounce through the air—depended on precise systems not yet tested.

As the CO2-heavy atmosphere whistled past the heatshield, alarms blared. A melted vane fragment had sheared the ship’s magnetorquer, their backup attitude control. Steadying manually, Raj fought headwinds while Elena jury-rigged inertial dampers to control descent angle.

“They’re not sending help, are they?” asked Amina, lungs burning from helmet recirculation systems. Elena chewed her lip, watching Edgeland Crater grow in her visor.

Finally, 1G. Wheels embedded in Martian silt.

---

**Epilogue: The New Earth**

They established *Spectre Base 1* at Earth’s designated coordinates, a single habitat dome powered by a limping reactor. Daily, Elena watched mission logs replayed on Earth—a montage of heroes sacrificing for humanity. Meanwhile, Snyder received a promotion.

The final transmission from Earth, 42 days post-landing, was a ping from her father, a raw text file in his obliterate-your-track vtk từng of communication: *”Taiwan shareholders pressured for Russian parts. Pat’s save the world’s, kid. Both had to be cut. –Dad”*

Elena stored it, overlaying a panoramic of Mars’ crimson dunes. They’d live. But humanity’s next step, she knew, would not be faster. It’d be warier—a slow, careful thing, where failure wasn’t hidden, but shared.

The stars watched, unblinking.

*Scene opens on a hushed Tokyo street, sunlight filtering through vacant storefronts. Kiyoharu, in his usual worn sweater and camera slung over his shoulder, stumbles upon a horde of shambling undead. His mouth drops in panic.*

**Kiyoharu:** (muttering, grabbing a fire extinguisher from a nearby dumpster) “What the hell…? This isn’t even Halloween…”

*He backs away,(camera whirring as he instinctively snaps a photo), but a groan cuts him off. A rotting hand lunges. Kiyoharu swings the extinguisher, cracking the skull with a sickening thud. Breathless, he stares at the twitching corpse.*

**Kiyoharu:** (voice shaking) “I’m… just a photography student. *Normal*, remember?!”

*A distant scream echoes. He peers around a corner, spotting a group of survivors—a nurse, a teenager, an elderly man—fleeing a swarm. Kiyoharu hesitates, then yanks off his jacket.*

**Kiyoharu:** (shouting over the chaos) “Hey! Over here! Grab that!” *He hurls the jacket like a distraction, drawing the undead’s attention. The group eyes him, wary.*

**Nurse:** “Who the hell are you?!”

**Kiyoharu:** (grinning nervously) “Kiyoharu! If you’re gonna die today, at least let me take a decent group photo first!”

---

*Days later, the survivors barricaded in a school gym. Kiyoharu, now makeshift leader, maps their escape routes on a chalkboard.*

**Kiyoharu:** (gesturing wildly) “Okay, so the harbor’s our best shot—boat, right? But we need to split up. Yuu, take the teens and flank east. Doc, secure the med supplies. And *you*—” *He gestures to the elderly man.* “—guard the ladder. …And maybe pipe down? You’re scarier than the zombies.”

*The group chuckles weakly. Kiyoharu’s camera captures their exhausted faces, framing them against shattered windows. He lingers on a photo of the nurse, her expression fierce but tired.*

**Kiyoharu:** (softly, to himself) “We can’t lose anyone else.”

---

- The truth unfolds in fragments: a viral leak from a biotech lab near Kiyoharu’s art school. The virus, designed to enhance cognitive function in animals, mutated after a lab technician—*his late father’s colleague—*accidentally exposed themselves. Guilt gnaws at him.*

**Kiyoharu:** (to the nurse, hiding a photo of his father) “They covered it up, didn’t they? My dad… he might’ve known.”

*The group storms the lab at dawn. Kiyoharu distracts guards while the nurse finds the virus logs. But as they download the data, the building erupts in flames. A infected guard corners Kiyoharu, his father’s face twisted grotesquely.*

**Kiyoharu:** (tearing up, raising the extinguisher) “Dad… I’m sorry I couldn’t save you.”

*He smashes the guard’s skull. The nurse tackles him as the lab collapses.*

---

*The survivors escape, data in hand. They regroup on a fishing boat, watching Tokyo burn. Kiyoharu develops the last roll of film—black-and-white images of their struggle, his father’s face among them.*

**Kiyoharu:** (to the group, tired but smiling) “We made it. Sorta. But… the world’s gonna hear about this. No more cover-ups.”

*The camera clicks. Somewhere in the ashes, a single zombie stirs—a remnant of the old world, now still. Kiyoharu’s lens captures its hollow, unblinking eyes.*

**Kiyoharu:** (whispering) “See ya later. I’ll Tweet about you.”

*Fade to black. The final photo fades in: the survivors, silhouetted against fire, shadows stretching behind them like old ghosts.*

- * Success? Failure? The truth remains… just out of focus.**

**End Scene**

*Kiyoharu’s arc closes—not with heroism, but with the quiet resolve of someone who learned to hold the line, one frame at a time.*

Kiyoharu’s arc closes—not with heroism, but with the quiet resolve of someone who learned to hold the line, one frame at a time.

**Scene: The Unseen Virus**

---

The city of Yuriko had always been a place of quiet order, its cobblestone streets lined with cherry blossom trees and its citizens moving like clockwork through their routines. But today, the air felt heavier, the sunlight too bright. Kiyoharu, a part-time librarian with a knack for fixing broken appliances, was walking home from the grocery store when the first screams pierced the stillness.

A figure stumbled into the street, face pale, eyes wide. “They’re *awake*,” the man gasped, before his body went rigid. His head snapped backward with a wet crack, and he lunged at a passerby, sinking yellow teeth into their throat.

Kiyoharu froze. Then, with a surge of adrenaline, he shoved an elderly woman out of the way as the infected mob swelled. “Get to the community center!” he shouted, grabbing a fire extinguisher from a nearby shop. “Barricade yourselves!”

---

**The First Stand**

By dusk, Kiyoharu’s makeshift militia of six—three teens, an off-duty nurse, a retired engineer, and two shopkeepers—had fortified the community center. The undead, sluggish but relentless, clawed at the boarded-up doors. The nurse, Emi, tended to a boy’s gash from a shattered window. “We can’t hold them here forever,” she said grimly.

Kiyoharu, armed with a crowbar, studied the chaos. “We need a plan. Where’s the outbreak starting?” The engineer, Takashi, pointed to the abandoned hospital on the hill. “They did weird experiments there years ago. Rumors said they were working on… something contagious.”

---

**The Truth Unearthed**

At dawn, Kiyoharu led a scouting party through smoke-choked streets. Inside the hospital, they found lab equipment scattered like toys, and a journal left open on a desk. *“Subject 001 exhibited full neural regeneration post-mortality. Containment breach imminent…”* The entries stopped abruptly. In a blood-splattered lab, they discovered a vial labeled *“VX-9: Neuroregenerative Agent.”*

A survivor—a trembling janitor—whispered that the lead scientist, Dr. Sato, had locked herself in the basement. “She said the virus was an accident,” he stammered. “A test gone wrong. She’s trying to destroy it.”

---

**The Final Battle**

The basement was a labyrinth of flickering lights and hissing pipes. Dr. Sato awaited them, surrounded by infected lab techs. “You can’t stop it,” she hissed, her own eyes already clouding with the virus. “The pathogen is airborne now.”

Kiyoharu’s group fought through the horde, but the doctor was already too far gone. “The antidote is in my desk,” she coughed, lunging. “Burn the lab. *Now.*”

As Takashi rigged explosives, Kiyoharu carried the antidote vial to the surface. The explosion shook the city, and the undead fell silent—then collapsed into ash.

---

**Epilogue: Dawn Over Yuriko**

The city survived, but not without scars. Kiyoharu, now hailed as a hero, stood on the hill overlooking the ruins of the hospital. Emi placed a hand on his shoulder. “You saved us,” she said.

He shook his head. “No. We saved each other.” The antidote had only been a myth—the virus had simply burned itself out. But the truth lingered: humanity’s hubris had nearly destroyed them.

Kiyoharu pocketed the journal. Some truths were better buried. For now, Yuriko rebuilt. And in the quiet moments, he wondered if the virus was truly gone—or just sleeping.

---

**Outcome:** Success, but with sacrifice. The city is saved, but the origin of the outbreak remains a shadowy secret. Kiyoharu emerges as a leader, forever changed by the fragility of normalcy.