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Don't Include a Five (Part Two)
Given a vector A with at least one non-five, return vector B, with all fives excluded (not replaced by zeros).

24 days ago

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Don't Include a Five
Given a vector A, return vector B with all 5s replaced with 0s.

24 days ago

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High Five!
Write a function that takes a number x and returns y = 'High Five' if x is not equal to five. Return y = 'Denied' if the number ...

24 days ago

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A Five Introduction
Write a function that takes a number x as an input and returns the same value as y, unless x = 5, in which case the function sho...

24 days ago

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Estimating Monthly Electricity Cost for a Household Appliance
You recently bought an electric kettle for your kitchen, and you want to estimate how much it costs to run every month. The kett...

24 days ago

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Voltage Divider Calculation
A voltage divider is a simple circuit used to obtain a reduced voltage from a higher voltage source using two resistors in serie...

24 days ago

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LED Current Calculation
In an electrical circuit, the current (III) flowing through an LED is determined using Ohm’s Law: Where: I is the current ...

24 days ago

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Inductor Energy Storage Calculation
The energy (EEE) stored in an inductor is given by the formula: Where: E is the energy in joules (J) L is the inductance in...

24 days ago

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Calculate Charge Using Capacitance and Voltage
The charge (Q) stored in a capacitor is given by the formula:Q=C×V where: C is the capacitance (in farads) V is the voltage (...

24 days ago

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Energy Stored in a Capacitor
The energy (E) stored in a capacitor is given by the formula: where: C is the capacitance (in farads) V is the voltage (in ...

24 days ago

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Calculate Current in a Series Circuit Using KVL
Kirchhoff's Voltage Law (KVL) states that the sum of voltages around a closed loop is zero. Given a voltage source (V) and three...

24 days ago

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Calculating the Total Resistance in a Series Circuit
Description: In a series circuit, the total resistance is the sum of the individual resistances. This problem asks you to write ...

24 days ago

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Simple Electrical Power Calculation
Calculate the electrical power using the formula: P=V×I where: V is the voltage (in volts) I is the current (in amperes)

24 days ago

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Ohm’s Law - Calculate Resistance
Ohm’s Law states that resistance R can be calculated as:R=V/I where: V is the voltage (in volts) I is the current (in ampere...

24 days ago

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Estimating Battery Lifetime Based on Load Profile and Depth of Discharge (DoD)
In a Battery Management System (BMS), the lifetime of a battery depends on various factors, including the Depth of Discharge (Do...

24 days ago

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Estimating the Range of an Electric Vehicle (EV)
In Electric Vehicles (EVs), the driving range is the estimated distance a vehicle can travel on a fully charged battery. The ran...

24 days ago

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Estimating Battery Backup Time for an Inverter
In a Battery Management System (BMS), estimating the backup time of a battery-powered inverter helps determine how long it can s...

24 days ago

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Battery Charge Rate Calculation
In a Battery Management System (BMS), the charge rate () of a battery can be calculated using the formula: where: is th...

24 days ago

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Battery State of Health (SoH) Calculation
In a Battery Management System (BMS), the State of Health (SoH) of a battery is an indicator of its overall condition. It is cal...

24 days ago

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Battery Charge Efficiency Calculation
In a Battery Management System (BMS), the efficiency of battery charging can be estimated using the formula: where: is the...

24 days ago

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Battery Voltage Drop Estimation
In a Battery Management System (BMS), the voltage drop (V_drop) due to the load can be calculated using the formula:V_drop=I×R ...

24 days ago

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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...

24 days ago

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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...

25 days ago

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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...

25 days ago

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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 ...

25 days ago

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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 : ...

25 days ago

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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...

25 days ago

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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...

25 days ago

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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...

25 days ago

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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...

25 days ago