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The Case of the Missing Prototype – Identify the Thief by Comparing Suspects’ Evidence and Alibi Scores
After gathering fingerprints, alibis, sensor data, and digital clues, it’s time to pinpoint the thief. You have a struct array ...
2 months 前
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The Case of the Missing Prototype – Extract the Culprit’s Name from a Mixed Letter-and-Number Email Message
While tracing the suspect’s digital footprint, you recover an email containing a mixed string of letters and numbers.The letters...
2 months 前
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The Case of the Missing Prototype – Calculate the Car’s Average Speed Between GPS Readings to Trace the Escape Route
Using GPS data, you’ve obtained the total distance (in meters) traveled by the suspect’s car at equal time intervals.These readi...
2 months 前
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The Case of the Missing Prototype – Detect Tampered Sensor Readings from the Stolen Device’s Data Logs
You’ve recovered partial sensor data from the stolen prototype.Each reading is stored in a numeric vector data, but something se...
2 months 前
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The Case of the Missing Prototype – Check for Overlapping Alibis Between Suspects to Spot Inconsistencies
Each suspect in the case has provided an alibi — a time interval [start end] representing when they claim to have been elsewhere...
2 months 前
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The Case of the Missing Prototype – Restore the Correct Frame Order from the Corrupted Security Camera Footage
You’ve finally recovered the security camera footage from the Innovation Lab,but the system malfunctioned and stored frames in t...
2 months 前
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The Case of the Missing Prototype – Match the Footprints Found in the Lab to the Suspects’ Shoe Sizes
The dust on the Innovation Lab floor reveals several footprints.You’ve measured their shoe sizes and noted them in a vector size...
2 months 前
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The Case of the Missing Prototype – Decode the Secret Note Found on the Desk to Reveal a Hidden Message
On the lab desk, you discover a short note filled with strange letters. After examining it, you realize it’s written in a Caesa...
2 months 前
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The Case of the Missing Prototype – Check the Lab’s Logbook for Suspicious Late-Night Entries
After counting the fingerprints, you turn your attention to the security logbook.It records the entry hours (from 0 to 23) of ev...
2 months 前
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The Case of the Missing Prototype - Count the Fingerprints Found at the Lab Door to Begin Your Investigation
You arrive at the Innovation Lab where the secret prototype was stolen. The door has been dusted for fingerprints, and a technic...
2 months 前
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Linear primes p' = mp + n
Problem statement List the prime numbers of the form p' = mp + n for a given (m,n) couple and such that p' < k, k positive in...
2 months 前
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List the complementary / symetric prime couples
Problem statement For a given positive integer n, provide the prime couples (p,p') such that p + p' = 10^n. NB : a number li...
2 months 前
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Check Legendre's conjecture
Context and problem statement Legendre's conjecture states for a given positive integer n, there always exists at least one pri...
2 months 前
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List the twin prime couples
Problem statement The twin prime couples (p,p') are the ones such that p' = p + 2. For a given integer n > 1, list the twin p...
2 months 前
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Check Bertrand-Chebyshev's theorem about prime numbers
Historical context Bertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory ...
2 months 前
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Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3
Problem statement For all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 : ...
2 months 前
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Check p = 4n +/- 1, the generic formula for odd prime numbers
Problem statement For all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 : Check this f...
2 months 前
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Chek the Delta = p' - p = 6k gap theorem about arithmetic progressions in the prime number set
Context In the prime numbers set there are some arithmetic progressions (sequences of three or more consecutive prime number...
2 months 前
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List the near-square primes, p = n² + 1 (Landau's 4th problem)
Historical context At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime...
2 months 前
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List primes which are the sum of two consecutive lower primes plus minus one
Problem statement Some prime numbers can be written as the sum of two consecutive lower primes plus / minus one : Like t...
2 months 前
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Battery Life Estimation for a Device
A battery-powered device consumes a constant current while operating. The estimated battery life (T) can be calculated using the...
2 months 前
